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date: 21 October 2017

Modeling the Impact of Environment on Infectious Diseases

Summary and Keywords

The introduction of pasteurization, antibiotics, and vaccinations, as well as improved sanitation, hygiene, and education, were critical in reducing the burden of infectious diseases and associated mortality during the 19th and 20th centuries and were driven by an improved understanding of disease transmission. This advance has led to longer average lifespans and the expectation that, at least in the developed world, infectious diseases were a problem of the past. Unfortunately this is not the case; infectious diseases still have a significant impact on morbidity and mortality worldwide. Moreover, the world is witnessing the emergence of new pathogens, the reemergence of old ones, and the spread of antibiotic resistance. Furthermore, effective control of infectious diseases is challenged by many factors, including natural disasters, extreme weather, poverty, international trade and travel, mass and seasonal migration, rural–urban encroachment, human demographics and behavior, deforestation and replacement with farming, and climate change.

The importance of environmental factors as drivers of disease has been hypothesized since ancient times; and until the late 19th century, miasma theory (i.e., the belief that diseases were caused by evil exhalations from unhealthy environments originating from decaying organic matter) was a dominant scientific paradigm. This thinking changed with the microbiology era, when scientists correctly identified microscopic living organisms as the pathogenic agents and developed evidence for transmission routes. Still, many complex patterns of diseases cannot be explained by the microbiological argument alone, and it is becoming increasingly clear that an understanding of the ecology of the pathogen, host, and potential vectors is required.

There is increasing evidence that the environment, including climate, can affect pathogen abundance, survival, and virulence, as well as host susceptibility to infection. Measuring and predicting the impact of the environment on infectious diseases, however, can be extremely challenging. Mathematical modeling is a powerful tool to elucidate the mechanisms linking environmental factors and infectious diseases, and to disentangle their individual effects. A common mathematical approach used in epidemiology consists in partitioning the population of interest into relevant epidemiological compartments, typically individuals unexposed to the disease (susceptible), infected individuals, and individuals who have cleared the infection and become immune (recovered). The typical task is to model the transitions from one compartment to another and to estimate how these populations change in time. There are different ways to incorporate the impact of the environment into this class of models. Two interesting examples are water-borne diseases and vector-borne diseases. For water-borne diseases, the environment can be represented by an additional compartment describing the dynamics of the pathogen population in the environment—for example, by modeling the concentration of bacteria in a water reservoir (with potential dependence on temperature, pH, etc.). For vector-borne diseases, the impact of the environment can be incorporated by using explicit relationships between temperature and key vector parameters (such as mortality, developmental rates, biting rate, as well as the time required for the development of the pathogen in the vector).

Despite the tremendous advancements, understanding and mapping the impact of the environment on infectious diseases is still a work in progress. Some fundamental aspects, for instance, the impact of biodiversity on disease prevalence, are still a matter of (occasionally fierce) debate. There are other important challenges ahead for the research exploring the potential connections between infectious diseases and the environment. Examples of these challenges are studying the evolution of pathogens in response to climate and other environmental changes; disentangling multiple transmission pathways and the associated temporal lags; developing quantitative frameworks to study the potential effect on infectious diseases due to anthropogenic climate change; and investigating the effect of seasonality. Ultimately, there is an increasing need to develop models for a truly “One Health” approach, that is, an integrated, holistic approach to understand intersections between disease dynamics, environmental drivers, economic systems, and veterinary, ecological, and public health responses.

Keywords: mathematical model, compartmental models, vector-borne diseases, water-borne diseases, zoonosis


During the 19th and 20th centuries, the burden of infectious diseases and their associated mortality greatly decreased, especially in developed countries (Brachman, 2003; Dye, 2014; Satcher, 1995). This was the natural consequence of the introduction of pasteurization, improved sanitation and hygiene, better education, and vaccination campaigns, all followed by the antibiotics era. This headway led to the perception that infectious diseases would progressively become a marginal problem for humanity (Brachman, 2003). Despite the tremendous advances of medicine and public health, infectious diseases still have a significant impact on morbidity and mortality in the 21st century globally. For instance, according to one estimation, in 2011 infectious diseases in the United Kingdom, a highly developed country, accounted for 7% of deaths and annual costs of £30bn (Davies, 2013).

Infectious diseases have not declined as expected. There are several reasons (Dye, 2014), including the urgent problems of the emergence and reemergence of new pathogens (Morse, 1995) and the spread of antibiotic resistance (CDC, 2015). Other important factors, however, are challenging the control of established, emerging and reemerging infectious diseases, including natural disasters, extreme weather, economic changes and poverty, commerce, international travel, and mass and seasonal migration; as well as the displacement of refugees owing to conflict and violence; rural–urban encroachment on human demographics and behavior; technology and industry globalization; breakdown in public health measures and infrastructures; climate change; deforestation and replacement with crop farms; disruption and contamination of water bodies; interaction between infectious and noninfectious diseases; and El Niño southern oscillations. The impact of some of these factors is discussed in Dye (2014); Eisenberg et al. (2007); Jones et al. (2008); Macpherson (2005); Morse (1995); and Patz, Graczyk, Geller, and Vittor (2000).

All these factors demonstrate the strong links, either directly or indirectly, between the environment and infectious diseases (Ayres, Harrison, Maynard, McClellan, & Nichols, 2010). Clearly, the word “environment” in this context has multiple meanings (see the discussion in Johnson et al., 1997). Here, “environment” refers to “the complex of physical, chemical, and biotic factors that act upon an organism or an ecological community and ultimately determine its form and survival” (Britannica, 2001). Of course, the strong interconnections between the environment and social, economic, and cultural factors are also important.

Although our understanding of the routes of transmission and the diverse abilities of pathogens to survive and grow in different environments has improved, there are still many unanswered questions. In particular, mathematical modeling is an important tool to help the scientific, medical, and public health community explore and possibly address these broad questions. Presented here, after a brief background, are some key examples demonstrating the potential of mathematical modeling in understanding the impact of the environment on infectious diseases.

From Miasma Theory to Advanced Theoretical Frameworks

Miasma Theory, Contagion Theory, Germ Theory, and Back to Environment

The link between the physical environment and diseases has been postulated since ancient times (Geller, 2001), as is revealed, for instance, by the etymology of some common names for infectious diseases: “malaria” comes from the Italian mala aria meaning bad air, as the disease was thought to be caused by foul air in marshy areas; “influenza,” a word from the Latin influentia, reflected the belief that the disease was caused by astrological and/or atmospheric influences; while the English word, “cold,” is self-explanatory. Other historical sources confirm the long-standing belief of the connection between environment and diseases: Empedocles (490–440 bc), according to Diodorus, managed to make the Sicilian city of Selinunte a healthy town by diverting two rivers so as to drain the local swamp land and improve the quality of the water supply (Stathakou, Stathakou, Damianaki, Toumbis-Ioannou, & Stavrianeas, 2009). This is thought to be one of the first known public health projects in history and implies attribution of a disease (malaria) to a source (swamp water), although it took more than 2000 years to identify the vector. Similarly, Hippocrates (460–370 bc) recommended to his medical followers that they should study the effects of the seasons, the hot and cold wind, and water on health (Hippocrates, trans. 1868).

Diseases were supposedly caused by evil exhalations from unhealthy environments that originated from decaying organic matter. This is the essence of “miasma theory” whose origins can be traced back to ancient times, although the term “miasma” (plural “miasmata” or “miasmatas”) probably did not appear for the first time until the 17th century (Collins English Dictionary, 1992). The theory was made explicit in 1717 by Giovanni Lancisi in his treatise De noxiis paludum effluviis (Of the poisonous effluvia of malaria; Porta, 2014). Miasma theory remained the dominant paradigm for centuries (Cipolla, 1992; Halliday, 2001; Howard-Jones, 1984), despite contemporaries’ awareness of its limitations. This is illustrated by a letter written in 1844 by an academic to the architecture journal, The Builder, describing miasmas as “unseen and subtle causes of disease, the existence of which we reason by analogy, and of which much has been said, although little is known” (Booth, 1844). In this letter, the author correctly advocates more salubrious buildings by ensuring adequate ventilation, effective drainage, reduced overcrowding, and so on (despite the scientific flaws in the theory exemplified by, nowadays humorous, statements such as “from inhaling the odour of beef the butcher’s wife obtains her obesity”; Booth, 1844, p. 350).

Undeniably, public health campaigns based on the flawed miasma theory effectively controlled many significant communicable pathogens (Cipolla, 1992; Eisenberg et al., 2007). Based on this fundamentally erroneous paradigm, during the 15th and 17th centuries, the states of northern and central Italy created an advanced system of public health and hygiene with the establishment of permanent health boards (magistracies) in the major cities (Cipolla, 1992). These boards would promote a variety of measures either during epidemics (administration of lazzarettos, creation of cemeteries reserved for the burial of plague victims etc.) or between epidemics (concerned with quality checks of food on sale, movement of beggars and prostitutes, quarantine of ships, sewers, etc.). Similarly, in 19th-century Britain, Sir Edwin Chadwick, one of the most important public health activists, social reformer, and confirmed believer in miasma theory, in his “Report on the Sanitary Conditions of the Labouring Population,” appropriately recommended measures such as the compulsory removal of all rubbish, improvement of drainage, ventilation, and street cleaning (Cipolla, 1992).

Even more remarkably, miasma theory was applied to the cholera outbreak in London in 1849 and was successfully supported by statistical models (Langmuir, 1961). More precisely, the great epidemiologist and statistician, William Farr, postulated that miasmas of cholera emanated from the River Thames and spread out over the various areas of the city. The spreading of miasmas was supposed to proportionally decrease with the elevation of the area above the Thames. Farr aggregated the cholera mortality for each district according to their elevation. This resulted in a clear correlation between cholera mortality and elevation above the River Thames with impressive agreement with observed data, as shown in Figure 1 (Farr, 1852; Langmuir, 1961).

Modeling the Impact of Environment on Infectious DiseasesClick to view larger

Figure 1. Correlation of cholera mortality and elevation above the Thames River, London, 1849, as calculated by William Farr. Data extracted from Farr’s original report (Farr, 1852). See also Langmuir (1961). For visual purposes, the x-axis was square-root transformed.

The contagious nature of diseases (i.e., the ability to transmit from person to person via physical contact) has also been recognized for a long time. According to Thucydides’ detailed description of the Plague of Athens (430–428 bc) during the Peloponnesian War “there was the awful spectacle of men dying like sheep, through having caught the infection in nursing each other” (Thucydides, trans., 1933, p. 131). Thucydides also showed an understanding of cross-species transmission when he wrote: “All the birds and beasts that prey upon human bodies, either abstained from touching them (though there were many lying unburied), or died after tasting them. In proof of this, it was noticed that birds of this kind actually disappeared; they were not about the bodies, or indeed to be seen at all” (Thucydides, trans. 1933, p. 131). Thucydides, however does not propose any hypothesis to explain the causes of disease, stating: “All speculation as to its origin and its causes, if causes can be found adequate to produce so great a disturbance, I leave to other writers, whether lay or professional; for myself, I shall simply set down its nature, and explain the symptoms by which perhaps it may be recognised by the student, if it should ever break out again” (Thucydides, trans., 1933, p. 129).

In contrast, the Roman writer Marcus Terentius Varro (116–127 bc), in his book De Re Rustica (On Agriculture), clearly expresses the idea that diseases were caused by contact with tiny, invisible living organisms, according to whom “[p]recautions must also be taken in the neighborhood of swamps, both for the reasons given, and because there are bred certain minute creatures [animaculae in Latin] which cannot be seen by the eyes, which float in the air and enter the body through the mouth and nose and there cause serious diseases”(Loeb, Goold, & Hooper, 1934). A concept also referred to as “seeds of diseases,” which had supporters since ancient Greek times, was fully elaborated by the physician and mathematician Girolamo Fracastoro (1478–1553; Nutton, 1983), who distinguished three forms of contagion: direct contact (typical of syphilis and gonorrhea); transmission by fomites; and infection at distance mediated by air (typical of tuberculosis and smallpox; Karamanou, Panayiotakopoulos, Tsoucalas, Kousoulis, & Androutsos, 2012). Fracastoro argued that infections are caused by transferable seed-like beings, although these seeds are conceived not as living microorganisms but as chemical substances liable to evaporation and atmospheric diffusion (Karamanou et al., 2012). Thus, the concept of disease transmission and contagion was well understood before microorganisms were actually identified.

The existence of microscopic organisms was revealed by Anton van Leeuwenhoek (1632–1723) using simple microscopes; he observed bacteria and protozoa, although he made no connections between these organisms and disease. Even when later scientists observed microorganisms in the blood of diseased people, the belief was that these microorganisms spontaneously generated because of the disease, rather than the other way round (“Germ Theory,” n.d.). The “spontaneous generation” theory, according to which life arises spontaneously from nonliving matter, remained the theoretical paradigm until the experiments of Francesco Redi (1626–1697) in 1668; Redi disproved the theory for higher organisms such as flies. And finally Louis Pasteur (1822–1895), in 1859, disproved the theory for microorganisms such as bacteria. Following this research, Pasteur proposed that microorganisms are the cause of diseases (“germ theory”). At the same time, Robert Koch (1843–1910) formulated the criteria and procedures (Koch’s Postulates) necessary to establish that a particular microbe and no other was the cause of a particular disease (Karamanou et al., 2012).

The laboratory-based research of Robert Koch and Louis Pasteur, which provided the scientific proof for the germ theory, was also complemented by the epidemiological work (i.e., the study of epidemic disease, including its spread, causes, and methods of control) of John Snow during the 1854 London cholera epidemic. Snow postulated that cholera was caused by contagious agents, which multiplied in an ill individual; these agents were transmitted by a direct fecal-oral route and through the contamination of the water supply, see, for example, Fisman (2007). Snow’s explanation, which Farr eventually accepted and supported, was correct. The comma-shaped bacillus Vibrio cholera was isolated in 1854 by Filippo Pacini (1812–1883), although his contribution was only recognized posthumously. It is unlikely that John Snow and Robert Koch (Koch also identified the agent Vibrio cholera 30 years later) were aware of Pacini’s paper (Howard-Jones, 1984).

The extensive work on cholera was pivotal in shifting from miasma theory, which is intrinsically associated with environmental factors (e.g., proximity to marshy areas, presence of smell), toward the germ theory paradigm, which correctly focused on microscopic organisms as pathogenic agents rather than the environment (still, in the 1874 international sanitary conference, representatives of 21 governments voted unanimously that “ambient air is the principal vehicle of the generative agent of cholera” (Howard-Jones, 1984, p. 380).

Yet, microbiological arguments alone are not sufficient (nor necessary as William Farr’s miasmatic model of cholera demonstrated (Langmuir, 1961) to explain the geographic distribution and seasonality of many infectious diseases (Altizer et al., 2006; Fisman, 2007). Recognition of the ecology (i.e., study of the relationships between organisms and their environment) of host and pathogen represents an important conceptual advancement, reconciling the microbiology paradigm (i.e., infections are caused by living organisms) with the observation that the patterns of many diseases are often associated with environmental factors. This theory is supported by increasing evidence that the environment can affect pathogen abundance, survival, or virulence, as well as host susceptibility to infection (Fisman, 2007), leading to the general consensus that environmental factors, including climate change, are one of the main drivers of disease emergence.

Accordingly, many conceptual frameworks to identify the impact of environmental factors on infectious disease have been proposed (Eisenberg et al., 2007). The objective of understanding and mapping the impacts of the environment on infectious diseases, however, is far from accomplished. Mathematical and statistical approaches are powerful tools to investigate this impact, but they still face many challenges (Lo Iacono et al., 2017). Table 1 lists some of these challenges

Table 1. Some challenges for mathematical modelers to estimate the impacts of environmental change on infectious diseases (these and other more technical, though important, challenges are discussed in the systematic review by Lo Iacono et al. (2017).

Disentangling multiple transmission pathways and identifying the biophysical mechanisms of how the environment affects disease and seasonality.

Reducing uncertainty and bias in reporting, which can mask the impact of environment.

Developing quantitative frameworks to study the potential effect on infectious diseases due to anthropogenic climate change, evaluating intervention, adaptation, and co-benefits

Identifying and quantifying the different sources of the temporal lag (e.g., the time required for potential growth of pathogen population in the environment, exposure dynamics, incubation period, delays in reporting) from the start of the pathway to infection to disease detection.

Studying the evolution of pathogen in response to climate and other environmental changes.

Investigating the effects of time-varying factors (e.g., seasonal exposure to a risk factor) on transmission patterns.

Dealing with different spatiotemporal scales (e.g., daily stochastic fluctuations, seasonal variation, or longer term El Niño oscillations.

Developing models for a truly One Health (Rabinowitz et al., 2013; Zinsstag et al., 2012) approach, that is,, an integrated, holistic approach to understand intersections between disease dynamics, environmental drivers, economic systems, and veterinary and public health responses.

Overcoming difficulties in acquiring suitable datasets to base the model on or test hypothesized associations between disease rates and weather.

A Brief Overview of Mathematical Modeling and Infectious Diseases

Models, by definition, are simplified frameworks describing natural phenomena. In particular, they have been used successfully to understand the dynamics of infectious diseases. The scope of mathematical modeling is broad: models can provide precise predictions, assessments of risk, tests of conjectures and hypotheses, and estimation of unknown parameters for statistical inference (i.e., drawing conclusions based on data), or they can simply offer heuristic insights (Hethcote, 2000). Process-based models are theoretical representations of the biophysical mechanisms under investigation (Dubitzky, Wolkenhauer, Cho, & Yokota, 2013). These models usually arise from first principles and/or are based on the empirical functions describing the fundamental processes (e.g., a phenomenological curve describing how the growth rates of certain pathogens depend on temperature or relative humidity). Process-based models are particularly suited to incorporate specific responses to altered environmental conditions; and they offer significant advantages in predicting the effects of global change as compared to purely statistical or rule-based models based on previously collected data (Cuddington et al., 2013).

An important class of process-based models is the group of compartmental models. In these types of models, the population of interest is usually partitioned into relevant epidemiological categories, such as susceptible, exposed, infected, and recovered individuals, see Box 1 and Figure 2 (Anderson & May, 1981, 1991; Hethcote, 2000; Keeling & Rohani, 2008). Key tasks of these compartmental models are to model transitions from one category to another and to calculate changes (such as population size and age composition) for each category (Box 1 and Figure 2). There are different methods to achieve these tasks. Some examples are illustrated in Table 2.

Modeling the Impact of Environment on Infectious DiseasesClick to view larger

Figure 2. Schematic of compartmental models with Environment compartment.

Table 2. Some examples of different, general, methods also used within the scope of compartmental models (other than solving differential equations).

Agent-Based Models

Agent-Based Models can be used to mimic the relevant processes with a computationally aided set of autonomous, interacting agents, for example, individuals belonging to a particular epidemiological category (Macal & North, 2010).

Network Analysis

Network Analysis focuses on the connections between individuals to study how infectious disease propagates (Danon et al., 2011; Keeling, 1999).

Branching Processes

Branching Processes (Jacob, 2010) have been applied, in particular to estimate the probability of extinction of one of these epidemiological categories.

Hawkes Processes

In Hawkes Processes, the transition from the susceptible to the infected category is governed by Poisson processes, with a memory of past events when the rate of infection is changing because of past infection or the depletion of the susceptible category (see the section “How Can We Model the Impact of Animal Reservoir on Uuman Infections? ” and Lo Iacono et al. (2016).

Box 1: Compartmental Models in Epidemiology

Example: The Susceptible-Infectious-Recovered (SIR) Model with Demography for Directly Transmitted Diseases.

Let us consider a population of N individuals, that is, the host, subjected to an epidemic. The task of the model is to estimate, at any time t, the number of (usually as a proportion of the total population size N): (i) infected, I; ii) susceptible, S (i.e., naïve individuals not previously unexposed to the disease, who can be infected by a contact with an infected individual); and (iii) recovered, R (those who cleared the infection and have developed life-long immunity). Infected individual are also “infectious”; that is, they can transmit the infection for the entire duration of being infected. The host lifespan is assumed to be 1/μ‎; μ‎ also represents the crude birth rate, as well as the mortality rate for susceptible, infected, and recovered. This ensures that the population size N is not changing over time. Transmission occurs by random contacts between the susceptible and infected populations with infection rate β‎. The recovery rate is denoted by γ‎. The incubation period of the infectious agent is instantaneous. There is no age, spatial, or social structure. Under these assumptions, the number of susceptible, infected, and recovered individuals can be obtained by solving a system of three coupled nonlinear ordinary differential equations:

dSdt=μPopulationbirthrateNβSIRate at which healthindividuals become infectedμSMortality of susceptibleindividuals

dIdt=βSIRate at which healthindividuals become infectedγIRate at which infectiousindividual are recoveredμIMortality of infectedindividuals

dRdt=γIRate at which infectiousindividual are recoveredμRMortality of recoverdindividuals

The equilibrium (no longer temporal variations in the overall number of susceptible, infected, and recovered) is reached when dSdt=dIdt=dRdt=0. This occurs when the epidemic fades out (S = 1,I = 0,R = 0) at all subsequent times, or in an endemic situation with the coexistence of the constant number of susceptibles, infected, and recovered individuals (Keeling & Rohani, 2008).

An important tool used in epidemiology is the Basic Reproductive Number, R0, that is, the average number of secondary cases generated by one case over the course of its infectious period, in an otherwise uninfected population. For the current model, it can be shown that:


and the endemic equilibrium is stable if R0i»1; otherwise the disease-free equilibrium is stable.

Most compartmental models, however, are built over a set of differential equations describing the rate of change of the population in each category (Box 1 and Figure 2) (Anderson & May, 1981, 1991; Hethcote, 2000; Keeling & Rohani, 2008). By solving the system of differential equations, it is possible to estimate the number of individuals in each compartment at any one time. Although a model for smallpox was already formulated and solved by Daniel Bernoulli in 1760 (Heesterbeek & Roberts, 2015; Hethcote, 2000; Murray, 2002), the roots of these compartmental models can be traced back to the beginning of the 20th century due to the work of Kermack and McKendrick (1927), Ross, Macdonald, and several other mathematicians and scientists (Smith et al., 2012). This class of models has been widely extended to other situations, including stochastic effects (Keeling & Ross, 2008), spatial variability, and other forms of heterogeneity in the network of contacts (Keeling, 1999), multiple species (Dobson, 2004), and evolutionary dynamics (Day & Gandon, 2007; Day & Proulx, 2004; Lo Iacono, van den Bosch, & Gilligan, 2013; Lo Iacono, van den Bosch, & Paveley, 2012).

Incorporating the Impact of Environment into Compartmental Models: Two Examples

Incorporating the Impacts of Environment in Models for Vector-borne Diseases

Climate and ecosystem change and globalization are impacting the ecology of arthropod species, and thus the occurrence of vector-borne diseases. Climate change has been shown to modify the geographic distribution of arthropod species: temperature and other weather variables directly affect their survival, reproduction, and biting rates, while changes in the availability and size of water bodies (due to new irrigation patterns, dam constructions, and changes in rainfall patterns) affect the accessibility to breeding sites and the rate at which the vectors lay their eggs. Temperature also affects the period between the infection of and transmission from vectors (i.e., pathogen extrinsic incubation periods), which usually require pathogen replication at ambient temperatures.

The impact of environment is often introduced directly in the epidemiological (and/or ecological) parameters in the compartmental models (e.g., in the infection rate β‎ and recovery rate γ‎ in Box 1) An increasing number of eco-epidemiological models for vector-borne diseases explicitly include the population dynamics of the vectors in the models. This can be done by using stage-structured models (see, e.g., Tuljapurkar & Caswell, 1997), where the population of a vector (e.g., mosquitoes) is partitioned into its different life stages—the egg, larva, pupa, and adult stages. These approaches typically model transitions from one stage to another, and calculate changes in the population size for each stage (e.g., Otero, Schweigmann, & Solari, 2008; Otero, Solari, & Schweigmann, 2006).

Important input parameters explicitly depend on weather variables. For example, the oviposition rate depends on the availability and size of the water bodies, which in turn depend on the precipitation and hydrology of the region (Asare, Tompkins, Amekudzi, Ermert, & Redl, 2016; Shaman, Spiegelman, Cane, & Stieglitz, 2006; Soti et al., 2012, 2013); the mortality and developmental rates, the biting rate, and the activity of the vectors depend on temperature and on other climatic variables; as well as the susceptibility of the vector to the pathogen and the extrinsic incubation period of the pathogen (the literature is vast; see, e.g., Rogers & Randolph, 2006, and the references therein). Explicit relationships are often available in the literature, and the time series of temperature could be readily used as model inputs, resulting in compartmental models with time-varying parameters (Box 2).

Box 2: Incorporating Weather Inputs in Epidemiological/Ecological Parameters

Example: Vector-borne Diseases

Potential input parameters for eco-epidemiological models for vector-borne diseases are the mortality, developmental rates, biting rates, and the activity of the vectors, as well as the extrinsic incubation period of the pathogen, depending on the temperature. These parameters are usually dependent on the temperature and other weather variables. The literature is vast and not reviewed here; only some examples are mentioned:

  • Temperature-dependent developmental rates. The developmental rates of the different stages of mosquitoes (egg, larva, pupa, adult) can be calculated, at least in laboratory conditions, from explicit temperature-dependent functions based on a physiological model for poikilotherm development. The developmental rate can be expressed as a nonlinear function of the ambient temperature with other species-specific parameters (i.e., the thermodynamics enthalpies and the temperature when half of the enzyme is deactivated because of high temperature) for which data are present in the literature (Otero et al., 6, 2008; Rueda, Patel, Axtell, & Stinner, 1990; Schoolfield, Sharpe, & Magnuson, 1981; Sharpe & DeMichele, 1977);

  • Temperature-dependent vector mortality, biting rate, and extrinsic incubation periods: The dependency of these quantities on temperature can be expressed as (a0a1T)b where T is the temperature and a0, a1, and b are constants, depending on the particular vector and pathogen (e.g., for mosquitoes/Rift Valley fever, see specific references cited in Fischer, Boender, Nodelijk, de Koeijer, and van Roermund (2013) and for Culicoides midges/African Horse Sickness, see specific references cited in Lo Iacono, Robin, et al. (2013).

Incorporating the Impact of Environment in Models for Water-borne Diseases

Other approaches directly model the dynamics of the pathogen population in the environment. Capasso and Paveri-Fontana (1979), for example, proposed a simple deterministic mathematical model for Vibrio cholerae, consisting of a system of two ordinary differential equations describing the change of the human-infected population in a town community and of bacterial abundance in the ocean. This naturally leads to an extension of the compartmental models by coupling the set of differential equations, similar to those shown in Box 1 and Figure 2, with an additional differential equation describing the concentration of the pathogen in the environment.

The set of equations can be explicitly regulated by environmental variables. For example, the growth and survival of V. cholera can be modeled based on inputs of weather and/or climatic drivers such as temperature, salinity, sunlight, and pH (Lipp, Huq, & Colwell, 2002). Precipitation is also expected to alter the contact rates between the contaminated water and the hydrological connections of local human populations (Righetto et al., 2013). Infections occur when a susceptible individual comes in contact with this additional category. Infected people can excrete pathogens, and this feeds back into the environmental compartment. Human-to-human transmission has also been incorporated in these models by allowing for infection transmission when a contact between a susceptible and infected person occurs.

This class of models, largely applied to Vibrio cholerae (Gatto et al., 2012; Righetto et al., 2012, 2013; Torres Codeco, 2001), is particularly suitable for the study of the impact of the environment on water-borne disease. Nevertheless, the environment can have an indirect impact on the epidemiology of these diseases, for example, by changing the population size (e.g., due to increased urbanization) and the rates of contact among people, or by altering the patterns of contact at the people–environment interface, leading to models that include human behavior such as population mobility (Mari et al., 2012).

Some Challenges Ahead

Despite significant progress, the impact of the environment on infectious disease is still open to many questions. Here we discuss in more detail these broad issues and, in some cases, propose potential approaches to address these questions.

Environment as Biodiversity

Biodiversity or biological diversity refers to “the variability among living organisms from all sources including, among other things, terrestrial, marine and other aquatic ecosystems and the ecological complexes of which they are a part; this includes diversity within species, between species and of ecosystems” (Convention on Biological Diversity, Article 2).

Does an Increase in Biodiversity Reduce the Burden of Disease?

This concept is known as the “dilution effect.” According to this hypothesis, preserving intact ecosystems and their endemic biodiversity would generally protect against infectious, zoonotic (i.e., diseases transmitted from animal to humans) diseases (Civitello et al., 2015; Johnson, Ostfeld, & Keesing, 2015; Keesing et al., 2010; Lacroix et al., 2014; LoGiudice, 2003). Biodiversity is usually measured by the number of different species present in a particular location, which in turn is regulated by other factors such as climate and land use (Walther et al., 2002). Different mechanisms have been proposed to explain how biodiversity impacts disease transmission. For directly transmitted zoonotic disease, such as Hantavirus pulmonary syndrome, rodent hosts living in areas with high species richness are more likely to come in contact with heterospecific mammals (different biological species) and less likely to come in contact with rodent hosts of the same species. If the heterospecific mammals are not susceptible to the infection, they break the chain of transmission, reducing the burden of diseases among rodents and thus reducing the risk of spillover to humans (Clay, Lehmer, St. Jeor, & Dearing, 2009; Keesing et al., 2010). For vector-borne diseases, the dilution effect can be explained in terms of “wasted bites,” that is, when the vector preferentially feeds on a species that does not develop infection. Accordingly, in some communities in Africa, people keep cattle or sheep near their houses, assuming that this will distract mosquitoes carrying malaria away from people. Similarly, some midges show apparent preference for cattle over sheep, so in South Africa deploying cattle to protect sheep from bluetongue has been proposed as a way to control the disease (Nevill, 1978). Mammal biodiversity at the global scale, however, is associated with an increased risk of emerging zoonosis (Jones et al., 2008). Accurate measurements of the dilution effect are difficult, as longitudinal studies of infection prevalence on different hosts are required. Not surprisingly, this hypothesis is still a matter of debate, with only partial evidence supporting it (Bouchard-Côté & Jordan, 2012; Ostfeld, 2013; Randolph & Dobson, 2012, 2013; Salkeld, Padgett, & Jones, 2013).

Process-based models can provide useful insight into a sometimes polarized debate. A theoretical work on African Horse Sickness, a fatal viral disease transmitted and amplified by Culicoides biting midges, demonstrated that the influence of noncompetent hosts is complicated by two potential, but contrasting, effects: a dilution effect, whereby vectors exhibit a feeding preference for a noncompetent, nonequid host; and an amplification effect, whereby increased vertebrate–host densities result in increased vector abundance (Lo Iacono, Robin, Newton, Gubbins, & Wood, 2013). Lo Iacono et al. explored how the Basic Reproductive Number (Box 1) in the presence/absence of the noncompetent host changed under different scenarios, depending on how the abundance of Culicoides midges is affected by the density of the host and the different values of feeding preference toward a particular host. The authors showed that the dilution effect is not universal, but rather depends on the particular scenario and parameter values. The approach can also provide quantitative estimates for this potential effect: for example, how many noncompetent hosts are needed in a farm to ensure that the disease is mitigated.

How Can We Model the Impact of Animal Reservoir on Human Infections?

Zoonotic diseases are at the origin of the majority of human pathogens (see Jones et al., 2008, and references therein). Perhaps HIV-1 is the most spectacular case of a human pandemic that emerged from an endemic infection of chimpanzees in Central Africa. Measles, smallpox, and diphtheria are examples of established human diseases that probably have zoonotic origins (Slingenbergh, Gilbert, de Balogh, & Wint, 2004). The Severe Acute Respiratory Syndrome (SARS) and swine influenza pandemics demonstrate that, although the transmissions of pathogens from animals to humans (“spillovers”) are rare events, they can transmit worldwide rapidly and have devastating health impacts.

The lack of a satisfactory answer to simple questions, such as “why do certain zoonotic diseases remain confined in the region where they originated while others result in a pandemic?” shows the challenges that the scientific, medical, and public health communities face. Cross-species transmission is driven not only by the physiology of the hosts and the biology of the pathogens, but also by the complex interactions of many environmental factors. These comprise weather and climatic factors (e.g., precipitation affecting vegetation and in turn the abundance of rodents), ecological factors (e.g., the presence of hosts with differing degrees of susceptibility and periodicity in their abundance), epidemiological and genetic factors (e.g., a broad set of pathogen life histories and periodicity of infection prevalence), and anthropogenic activities (e.g., land-use and behavioral changes affecting direct and indirect interactions with reservoir hosts). Despite some theoretical progress (Blumberg & Lloyd-Smith, 2013; Cauchemez et al., 2013; Kubiak, Arinaminpathy, & McLean, 2010; Kucharski et al., 2014; Lo Iacono et al., 2016; Reluga & Shim, 2014), disentangling the many complex aspects of transmission at the animal–human interface is still a compelling task for future studies (Allen et al., 2012; Lloyd-Smith et al., 2009).

This issue is even more complicated when, as well as animal-to-human transmissions, human-to-human infections also occur, and the environment is likely to have a differential impact on these two routes of transmission. To address these tasks, Lo Iacono et al. (2016) proposed modeling these infections using a stochastic framework known as Hawkes Processes. According to this model, each infection is governed by a Poisson process; the rate of infections, however is not constant, but rather depends on the time-varying number of susceptibles and infected at each previous time step. New infections can generate other infections (“self-exciting process”) but may also cause the depletion of the susceptibles, with a damping effect on the progression of the infection (“self-correcting process”). The key environmental and socioeconomic processes can be incorporated into the time-dependent rate of infections in a simple manner (Box 3). The model can then be used to understand the potential different impacts of environmental drivers on the spillover from animal-to-human and human-to-human transmissions.

Box 3: The Impact of Environment on Spillover and Human-to-Human Transmission

Lo Iacono et al. (2016) modeled the risk of k spillovers during a specific period of time as a Poisson process with the rate of infections λ proportional to:


where NH is the human population size, that is, the total number of people in a suitable area such as a village;PrR(NR) is the infection prevalence in the animal reservoir; and ηR is a measure of exposure. The model was then extended by including the depletion of the susceptibles and human-to-human transmission.

Environmental drivers can be readily incorporated in the rate of infections. For example, complex social, economic, and political drivers affecting demographic patterns could be translated and quantified in terms of their impacts on the typical size of the human population (i.e., the factor NH). Economic and behavioral drivers (e.g., in the case of Lassa fever; the practice of burning fields after harvesting, driving the animal reservoir toward villages; young boys catching rodents as a recreational activity; and the seasonal crowding of miners in dwellings) could, be expressed in terms of their effects on the exposure to disease, that is, the factor ηR. Similarly, climatic and weather factors (e.g., rainfall increasing vegetation, thus enhancing food resources for the animal reservoir) can affect the abundance of the reservoir and thus the exposure. Ultimately, complex biological, physical, environmental, and social factors can be expressed as factors that can be either measured or quantified via independent models and then fed into the current modular approach.

Potential Impact of the Environment on the Evolution of Pathogens

There is now evidence that environmental factors in general and climate change in particular affect the geographical distributions and abundance of many species, including pathogens and vectors of diseases, as well as the timing of growth and reproduction (Altizer, Ostfeld, Johnson, Kutz, & Harvell, 2013; Hoffmann & Sgrò, 2011; Moritz & Agudo, 2013).There are different adaptive responses to environmental change (Hoffmann & Sgrò, 2011; Hoffmann & Willi, 2008; Santini, 2015). One response is to exploit phenotypic plasticity, that is, the capacity of a genotype (the entire set of genes of a living organism) to exhibit variable phenotypes (its physical characteristics) in different environments, enabling an individual to adapt to changed environments without the need for novel genetic mutations. Another is migration, directly or facilitated by vectors, to more suitable habitats. Another response is evolving new attributes, although direct evidence of genetically based adaptation to climate change over time remains limited (Moritz & Agudo, 2013).

Examples of evolutionary adaptation are mainly available in agro-ecosystems, owing to the large selection pressures originated by growing use of genetic technologies (e.g., the use of disease-resistant crops), the widespread use of chemical controls promoting herbicide and insecticide resistance, and intense changes in land use (Lo Iacono et al., 2012; Santini, 2015; Thrall et al., 2011). There are, however, other examples relevant to human health. For instance, in Bangladesh the dominant pathogenic strain for Vibrio cholera was the Classical strain until the 1970s; then the mutant El Tor strain invaded the resident population and replaced the Classical strain, which can be explained by changes in monsoon rainfall patterns (Koelle, Pascual, & Yunus, 2005). Another example is Lyme disease; according to Kurtenbach et al. (2006), the strains of the Lyme bacterium, Borrelia burgdorferi, are subjected to different selection pressures, depending on the synchrony and asynchrony of the seasonal activity of the larval and nymphal ticks. More precisely, “asynchrony of infecting nymphs and uninfected larvae favours pathogen persistence strategies, whereas synchrony of these tick stages combined with a short annual period of activity should favour short-lived ‘boom-and-bust’ strategies and the capacity for co-feeding transmission” (Kurtenbach et al., 2006, p. 666).

The patterns of seasonality are also expected to be an important driver of pathogen evolution (Altizer et al., 2006; Donnelly, Best, White, & Boots, 2013), as periods of high transmission are followed by “population bottlenecks,” reducing strain diversity and causing rapid genetic shifts (Patz et al., 2003). Another important example arises from the interaction between environmental and demographic stochasticity. More precisely, epidemics are characterized by stochastic fluctuations, with their own frequencies. These “natural frequencies” depend on the parameters of the system, for example, the infectious and incubation period, the birth rate of the host, and so on (see, e.g., Keeling & Rohani, 2008). When an external periodic perturbation, such as seasonality in temperature or in the application of control measures, has a frequency close to the natural frequencies of the epidemics, the result will be enhanced fluctuations in the epidemics (resonance), promoting the emergence or suppression of particular strains of the pathogen (Lo Iacono, van den Bosch, et al., 2013).

Mathematical modeling of multistrain, multi-host pathogens remains, in general, a major challenge (Dobson, 2004; Kurtenbach et al., 2006). Not surprisingly, extensions of this class of models in response to environmental and climate change are even more challenging.

Impact of the Environment on the Stability of Infectious Diseases and Their Potential Vectors

Let us consider vector-borne diseases again. Human mobility, wild and domestic animal trade, and climate change are increasing the opportunity for the vector, and also the pathogens, to reach and potentially become established in different parts of the globe. Several examples now support this position: the incursion of the mosquito Aedes albopictus (known vector of chikungunya virus, yellow fever virus, dengue virus, zika virus, and dirofilariasis) into Europe through the international trade in used tires and lucky bamboo (Medlock et al., 2012); outbreaks of mosquito-borne chikungunya fever in northeastern Italy in 2007 (Beltrame et al., 2007; Rezza et al., 2007); autochthonous cases of dengue fever in 2010 in France (La Ruche et al., 2010), in Croatia (Gjenero-Margan et al., 2011) and Madeira in 2012 (European Centre for Disease Prevention and Control, 2013; Tomasello & Schlagenhauf, 2013); and the unexpected, epizootics of Culicoides-borne viral diseases such as bluetongue and Schmallenberg virus (Koenraadt et al., 2014) in northern Europe probably due to climate change. These and other examples raise simple but only partially answered questions, some of which are listed in Box 4.

Box 4: Further Questions

  1. A. What makes an endemic area endemic? What is the likelihood that a new infection becomes endemic in a different part of the globe? These two questions are essentially equivalent. For vector-borne diseases, having a suitable habitat that guarantees the presence of vectors is a necessary condition; but this is not sufficient to ensure persistence of the infection. Furthermore, the generic expression of a “suitable habitat” needs to be translated into precise environmental information, such as the range of temperatures and relative humidity, patterns in precipitations, appropriate terrain to ensure availability of breeding sites, type of vegetation, and presence of vertebrate hosts.

  2. B. What happens if the system is perturbed? As an example, let us assume that the population of vectors is altered following the temporary use of chemical control or a temporary change in the agricultural irrigation patterns. In other words, the system is perturbed. Once any form of perturbation is suspended, would the abundance of vectors return to the same abundance as in the unperturbed situation? Similar types of questions are applicable to the pathogen dynamics.

  3. C. How will climate change impact patterns of infection? Climate change is not a mere increase in the average value of air temperature, and the average value of air temperature is not the only determinant affecting vector population and infectious diseases. For instance, the eggs of the Aedes mosquitoes require a minimum desiccation period; after this period, they are mature to hatch, provided they are submerged in water. This suggests that the potential changes in the frequency of fluctuating rainfall might also impact the population of Aedes mosquitoes. This might also introduce a change of the phase between seasonality in temperature (controlling developmental stage and mortality) and seasonality in rainfall (controlling the oviposition process). How this cascades on the mosquito population is unknown. Vectors can also be augmented by flooding. Of course, climate change is expected to also affect human behavior and cultural and socioeconomic factors (see point D.)

  4. D. How will other environmental, cultural, and socioeconomic factors impact on the disease? Many other factors act directly and indirectly as drivers of disease. For instance, the gathering of large numbers of people and domestic animals to be slaughtered during religious festivities has been identified as an important risk factor for Rift Valley fever. The construction of infrastructure such as dams or changes in irrigation patterns are other examples of socioeconomic activities associated with mosquito-borne diseases

Mathematically, the response of dynamic systems like infectious diseases to external changes can be addressed by using stability analysis (May, 2001). Stability analysis measures the resistance to change of the system under investigation. For nonseasonal compartmental models, stability analysis proceeds by (1) identifying the equilibrium solution, that is, when the populations in all the compartments (e.g., susceptible, infected, recovered) are no longer changing with time; and (2) checking if the solution is stable, that is, the system returns to the equilibrium solution after being perturbed. Examples of equilibrium solutions can be the situation when the diseases fade out or an endemic situation with fixed coexisting populations of infected and susceptible individuals.

A crucial aspect for many biological systems, however, is that these exhibit periodic patterns. Periodicity might arise from the seasonality in the environmental drivers or from the internal dynamics of the system such as predator–prey cycles. In the context of seasonal vector-borne diseases, the system might result, for instance, in sustained oscillations in the populations of vectors and/or infected individuals. As in the nonseasonal case, a key question is whether or not these periodic solutions are stable. This can be done by crude numerical simulations or, more elegantly, by employing Floquet Theory, a well-established mathematical tool that provides stability analysis for periodic systems (Grimshaw, 1993; Klausmeier, 2008). The biophysical interpretation of stability analysis is extremely important. For instance, through international trade, batches of mosquitoes imported into a naïve region could either fade out or grow, and after a transient phase, eventually the new species will invade and establish in the region. Stability analysis is able to quantify the range of the key environmental factors ensuring the extinction, establishment, or even chaotic behavior, of the mosquito population. The same analysis can be repeated, focusing on the pathogen dynamics rather than on the vectors.

Quantifying the Time Lag between Environmental Stimuli and the Occurrence of Disease

The effects of the environment on the occurrence of disease are not instantaneous. This issue is further complicated as multiple causal pathways can be involved. For instance, in the case of Lyme disease, a tick-borne disease, environmental factors such as temperature, day length, and relative humidity continuously affect the physiology of the ticks, namely, the developmental, diapause (i.e., a period of suspended development in an insect), and mortality rates (Belozerov, 2009; Dobson, Finnie, & Randolph, 2011; Dobson & Randolph, 2011; Gilbert, Aungier, & Tomkins, 2014; Knülle & Rudolph, 1982; Ludwig, Ginsberg, Hickling, & Ogden, 2016; Ogden et al., 2005; Oliver, 1989; Ostfeld & Brunner, 2015; Randolph, Green, Hoodless, & Peacey, 2002). These individual, not-instantaneous responses will have a detectable effect on the abundance and questing activity of the ticks only after a certain time lag. Environmental factors will change the behavior of people too (e.g., their choice of outdoor activity and type of clothing), affecting the chance of being bitten by an infected tick. Assuming that the tick bite results in an infection, this infection will not be detected until symptom onset, introducing a further time lag. Finally, the infection will be (hopefully) reported to the health authorities after a certain time lag, depending on the country’s health system (Dhôte, Basse-Guerineau, Beaumesnil, Christoforov, & Assous, 2000; Marinović, Swaan, van Steenbergen, & Kretzschmar, 2015). Furthermore, the typical incubation periods and disease notification depend on the particular clinical form of the infection (i.e., the incubation periods range from about two weeks for patients showing erythema migrans alone to 96 weeks for patients presenting with the neurological complications termed acrodermatitis chronica atrophicans (Dhôte et al., 2000).

Detection of diseases can also be affected by the environment. For example, it has been reported that the incidence of Lassa fever in Sierra Leone is higher during the dry season (Shaffer et al., 2014; Webb et al., 1986). Recent analyses, however, indicate that this could be an artifact of data collection methods, for example, because of impassable roads reducing the ability to seek medical care during the rainy season (Bausch, Moses, Goba, & Grant, 2013; Grant et al., 2016).

Thus, the time lag from some changes in the environmental factors triggering the causal pathways of infection (which can be challenging to define) to disease detection is the cumulative effect of many time lags arising from different sources. These are typically represented by random variables drawn from adequate distributions, for example, a log-normal distribution (Sartwell, 1995). This is more complicated if there are multiple routes of transmissions (e.g., human-to-human as well as animal-to-human or a water-reservoir-to-human), as this introduces further time lags from different origins. Estimating the time lag between an environmental variable and infection is a common task encountered in the literature. In most cases, the assessment is based on assessing potential correlations between the time series of disease incidence and the time series of environmental variables at 1,2 … n weeks before the date of the reported case. The methods used, however, rarely distinguish among the different sources of time lags, nor do they incorporate the mechanisms of these delays.

Environment and Human Behavior

The importance of human behavior in the progression of infectious diseases is unquestionable. Accordingly, a growing body of research is incorporating human and other animal behavioral changes into infectious disease models (Verelst, Willem, & Beutels, 2016). Many studies have focused on reactive behavioral change, such as vaccination prompted by the emergence of risk of infection. Further progress will come by validating these theoretical models with data (Verelst et al., 2016). This concern is expected to be valid for models of human behavior in response to environmental factors. However, some attempts in behavioral models have been validated with data. For example, as part of an exploration of the risk of African Horse Sickness transmission in Great Britain, Lo Iacono et al. (2013) modeled the likelihood of the location of horses in Great Britain based on simple assumptions of human behavior, data on land use, and qualitative data collection based on questionnaires.


Mathematical modeling is essential to understand the complex interaction between the environment (in the broad sense, including animals, humans, climate, etc.) and infectious diseases, and possibly predict its impact. Many significant questions remain, however; only a limited number of these issues are discussed and illustrated here. Apart from the expected problems associated with the development of new mathematical and computational techniques, these issues pose other challenges, which can be summarized as (1) undefined scope; (2i) limited data; and (3) partial attainment in developing a “One Health” approach.

Undefined Scope

The term “environment” is a collective word comprising many biological and physical factors. Behavioral and socioeconomic aspects also have direct and/or indirect links with the environment. For instance, economic and political reasons alone might promote the construction of a new dam or changes in irrigation patterns; this decision could result in critical changes in the environment that are likely to affect water-borne and vector-borne infectious diseases. Entangled multifactors are not the only source of ambiguity. Even when focusing on a single well-defined measurable driver, multiple effects are possible. For example, temperature directly changes the life history parameters of mosquitoes and associated diseases, but it can also affect human behavior. The first effect can be treated as a “dose-response relationship,” and its incorporation in mathematical models is relatively straightforward. In contrast, the inclusion of human behavior in mathematical approaches is still in its infancy and is seldom included in these models.

Limited Data

Within the United Kingdom, the hiatus caused by the bubonic plague in 1665 contributed to the routine collection of mortality data by cause of death, and Farr in the 19th century improved the provision of standardized disease surveillance data that is essential for disease epidemiology modeling and intervention. Data are still subjected to many limitations, however. “Disease reporting bias” is a well-known problem (Gibbons et al., 2014), and approaches to deal with surveillance artifacts such as bank holidays, vacations, travel, and weekends have been used (Nichols, Richardson, Sheppard, Lane, & Sarran, 2012). Reliable data on pathogen incidence are scarce, especially in developing countries, although this is expected to change with the advancement of genome sequences (Grad & Lipsitch, 2014) and improved surveillance efforts (Nichols, Andersson, Lindgren, Devaux, & Semenza, 2014). Weather data are relatively easy to collect; even so, they are subjected to important limitations. In developing countries, long-term, high-resolution weather data are often absent. In developed countries, the data might be available, but fine spatiotemporal linkage of these data with infection cases is rare (Djennad et al., 2017). For many diseases, the microclimate at the spatiotemporal domain where infection occurred (e.g., indoor temperatures and relative humidity) is important information. However, this type of information is seldom accessible. A similar problem is encountered when estimations of wildlife abundance and distribution of animal host are required.

Partial Attainment in Developing a Truly One Health Approach

The One Health perspective is a holistic approach that recognizes the interconnections between human health, animal health, and the environment, including socioeconomic factors. Despite a growing support for these integrated cross-disciplinary approaches (Restif et al., 2012), many One Health initiatives are still subjected to the barriers that segregate its contributing disciplines (Manlove et al., 2016). This is somehow expected, owing to researchers from different disciplines with different perspectives on approaches. They have been described as wanting to “share frameworks about as much as they like to share toothbrushes” (Gorman, Kincannon, & Mehalik, 2001).

Of course, the challenges in cross-disciplinary studies are not only a matter of scientists’ parochial attitudes. Developing a solid One Health approach, and even more for a Planetary Health approach, which extends the philosophy of One Health by focusing not only on the present generation but on past and future civilizations (Whitmee et al., 2015), requires clear conceptualization of the broad problem (i.e., to define the scope) and access to data from many sources—two key problems already discussed (sections “Undefined Scope” and “Limited Data”). It can be logistically and financially daunting. For instance, a three-year scientific grant is unlikely to be long enough for longitudinal model-guided fieldwork. The drawbacks of this partial integration inevitably will cascade into the selection of the modeling approaches. Despite these challenges, integrative approaches combining process-based, empirical, and participatory modeling have the potential to improve models by guiding the design of the models possibly anchored with data (Grant et al., 2016; Scoones et al., 2017).


This work was supported by the National Institute for Health Research Health Protection Research Unit (NIHR HPRU) in Environmental Change and Health at the London School of Hygiene and Tropical Medicine in partnership with Public Health England (PHE), and in collaboration with the University of Exeter, University College London, and the Met Office; and the UK Medical Research Council (MRC) and UK Natural Environment Research Council (NERC) for the MEDMI Project. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR, the Department of Health, or Public Health England.


Allen, L. J. S., Brown, V. L., Jonsson, C. B., Klein, S. L., Laverty, S. M., Magwedere, K., … van den Driessche, P. (2012). Mathematical modeling of viral zoonoses in wildlife. Natural Resource Modeling, 25(1), 5–51.Find this resource:

Altizer, S., Dobson, A., Hosseini, P., Hudson, P., Pascual, M., & Rohani, P. (2006). Seasonality and the dynamics of infectious diseases. Ecology Letters, 9(4), 467–484.Find this resource:

Altizer, S., Ostfeld, R. S., Johnson, P. T. J., Kutz, S., & Harvell, C. D. (2013). Climate change and infectious diseases: From evidence to a predictive framework. Science (New York), 341(6145), 514–519.Find this resource:

Anderson, R. M., & May, R. M. (1981). The population dynamics of microparasites and their invertebrate hosts. Philosophical Transactions of the Royal Society B: Biological Sciences, 291(1054), 451–524.Find this resource:

Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans: Dynamics and control. Oxford: Oxford University Press.Find this resource:

Asare, E. O., Tompkins, A. M., Amekudzi, L. K., Ermert, V., & Redl, R. (2016). Mosquito breeding site water temperature observations and simulations towards improved vector-borne disease models for Africa. Geospatial Health, 11(1s), 67–77.Find this resource:

Ayres, J. G., Harrison, R. M., Maynard, R. L., McClellan, R. P., & Nichols, G. L. (2010). Environmental medicine in context. In J. G. Ayres, R. M. Harrison, G. L. Nichols, & R. L. Maynard (Eds.), Environmental medicine.(pp. 3–22). London: Edward Arnold & Co.Find this resource:

Bausch, D. G., Moses, L. M., Goba, A., Grant, D. S., & Kahn H. (2013). Lassa fever. In S. Singh & D. Ruzek (Eds.), Viral hemorrhagic fevers (pp. 1–41). Boca Raton, FL: Taylor & Francis.Find this resource:

Belozerov, V. N. (2009). Diapause and quiescence as two main kinds of dormancy and their significance in life cycles of mites and ticks (chelicerata: Arachnida: acari). Part 2. Parasitiformes. Acarina, 17(1), 3–32.Find this resource:

Beltrame, A., Angheben, A., Bisoffi, Z., Monteiro, G., Marocco, S., Calleri, G., … Viale, P. (2007). Imported Chikungunya infection, Italy. Emerging Infectious Diseases, 13(8), 1264–1266.Find this resource:

Blumberg, S., & Lloyd-Smith, J. O. (2013). Inference of R0 and transmission heterogeneity from the size distribution of stuttering chains. PLoS Computational Biology, 9(5), e1002993.Find this resource:

Booth, A. (1844). Suggestions on the chemical characters of contagion, and the nature of the exhalation given off from the want of ventilation, drainage, and sewerage, and in the confined districts and abodes of the poor, &c. The Builder (Vol. 2, No. lxxv, pp. 350–351). Retrieved from this resource:

Bouchard-Côté, A., & Jordan, M. I. (2012). Evolutionary inference via the Poisson Indel process. Proceedings of the National Academy of Sciences of the United States of America, 110(4), 1160–1166.Find this resource:

Brachman, P. S. (2003). Infectious diseases—Past, present, and future. International Journal of Epidemiology, 32(5), 684–686.Find this resource:

The Editors of Encyclopædia Britannica (2001). Article: Environment, Encyclopædia Britannica, inc. Retrieved from

Brubaker, J. F., & Turell, M. J. (1998). Effect of environmental temperature on the susceptibility of Culex pipiens (Diptera: Culicidae) to Rift Valley fever virus. Journal of Medical Entomology, 35(6), 918–921.Find this resource:

Capasso, V., & Paveri-Fontana, S. L. (1979). A mathematical model for the 1973 cholera epidemic in the European Mediterranean region. Revue d’Epidémiologie et de Santé Publique, 27, 121–132.Find this resource:

Carpenter, S., Wilson, A., Barber, J., Veronesi, E., Mellor, P., Venter, G., & Gubbins, S. (2011). Temperature dependence of the extrinsic incubation period of orbiviruses in Culicoides biting midges. PloS One, 6(11), e27987.Find this resource:

Cauchemez, S., Epperson, S., Biggerstaff, M., Swerdlow, D., Finelli, L., & Ferguson, N. M. (2013). Using routine surveillance data to estimate the epidemic potential of emerging zoonoses: Application to the emergence of US swine origin influenza A H3N2v virus. PLoS Medicine, 10(3), e1001399.Find this resource:

Centers for Disease Control. (2015). About antimicrobial resistance. Retrieved from

Cipolla, C. M. (1992). Miasmas and disease: Public health and the environment in the pre-industrial age. New Haven, CT: Yale University Press.Find this resource:

Civitello, D. J., Cohen, J., Fatima, H., Halstead, N. T., Liriano, J., Mcmahon, T. A., … Rohr, J. R. (2015). Biodiversity inhibits parasites: Broad evidence for the dilution effect. Pnas, 112(28), 8667–8671.Find this resource:

Clay, C. A., Lehmer, E. M., St. Jeor, S., & Dearing, M. D. (2009). Sin Nombre virus and rodent species diversity: A test of the dilution and amplification hypotheses. PLoS ONE, 4(7).Find this resource:

Collins English dictionary (3d ed.). (1992). Glasgow, Scotland: HarperCollins.Find this resource:

Cuddington, K., Fortin, M.-J., Gerber, L. R., Hastings, A., Liebhold, A., O’Connor, M., & Ray, C. (2013). Process-based models are required to manage ecological systems in a changing world. Ecosphere, 4(2), art20.Find this resource:

Danon, L., Ford, A. P., House, T., Jewell, C. P., Keeling, M. J., Roberts, G. O., … Vernon, M. C. (2011). Networks and the epidemiology of infectious disease. Interdisciplinary Perspectives on Infectious Diseases, 2011, Article ID: 284909.Find this resource:

Davies, S. C. (2013). Infections and the rise of antimicrobial resistance. Annual report of the chief medical officer. Volume Two, 2011, Infections and the rise of antimicrobial resistance. Retrieved from this resource:

Day, T., & Gandon, S. (2007). Applying population-genetic models in theoretical evolutionary epidemiology. Ecology Letters, 10(10), 876–888.Find this resource:

Day, T., & Proulx, S. R. (2004). A general theory for the evolutionary dynamics of virulence. American Naturalist, 163(4), E40–E63.Find this resource:

Dhôte, R., Basse-Guerineau, A. L., Beaumesnil, V., Christoforov, B., & Assous, M. V. (2000). Full spectrum of clinical, serological, and epidemiological features of complicated forms of Lyme borreliosis in the Paris, France, area. European Journal of Clinical Microbiology and Infectious Diseases: Official Publication of the European Society of Clinical Microbiology, 19(11), 809–815. Retrieved from this resource:

Djennad, A., Lo Iacono, G., Sarran, C., Kessel, A., Haines, A., Fleming, L. E., & Nichols, G. L. (2017). A comparison of weather variables linked to infectious disease patterns using laboratory addresses and patients’ home addresses. BMC Infectious Diseases.Find this resource:

Dobson, A. (2004). Population dynamics of pathogens with multiple host species. The American Naturalist, 164 (S5), S64–S78.Find this resource:

Dobson, A. D. M., Finnie, T. J. R., & Randolph, S. E. (2011). A modified matrix model to describe the seasonal population ecology of the European tick Ixodes ricinus. Journal of Applied Ecology, 48(4), 1017–1028.Find this resource:

Dobson, A. D. M., & Randolph, S. E. (2011). Modelling the effects of recent changes in climate, host density and acaricide treatments on population dynamics of Ixodes ricinus in the UK. Journal of Applied Ecology, 48(4), 1029–1037.Find this resource:

Donnelly, R., Best, A., White, A., & Boots, M. (2013). Seasonality selects for more acutely virulent parasites when virulence is density dependent. Proceedings. Biological Sciences/The Royal Society, 280(1751), 20122464.Find this resource:

Dubitzky, W., Wolkenhauer, O., Cho, K.-H., & Yokota, H. (Eds.). (2013). Encyclopedia of systems biology. New York: Springer.Find this resource:

Dye, C. (2014). After 2015: infectious diseases in a new era of health and development. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 369(1645), 20130426.Find this resource:

Eisenberg, J. N. S., Desai, M. A., Levy, K., Bates, S. J., Liang, S., Naumoff, K., & Scott, J. C. (2007). Environmental determinants of infectious disease: A framework for tracking causal links and guiding public health research. Environmental Health Perspectives, 115(8), 1216–1223.Find this resource:

European Centre for Disease Prevention and Control. (2013). Mission report. Dengue outbreak in Madeira, Portugal. October–November 2012. European Centre for Disease Prevention and Control, Stockholm.Find this resource:

Farr, W. (1852). Report on the mortality of cholera in England, 1848–49. Great Britain. General Register Office. London: W. Clowes. Retrieved from this resource:

Fischer, E. A., Boender, G.-J., Nodelijk, G., de Koeijer, A. A., & van Roermund, H. J. (2013). The transmission potential of Rift Valley fever virus among livestock in the Netherlands: A modelling study. Veterinary Research, 44(1), 58.Find this resource:

Fisman, D. N. (2007). Seasonality of infectious diseases. Annual Review of Public Health, 28, 127–143.Find this resource:

Gatto, M., Mari, L., Bertuzzo, E., Casagrandi, R., Righetto, L., Rodriguez-Iturbe, I., & Rinaldo, A. (2012). Generalized reproduction numbers and the prediction of patterns in waterborne disease. Proceedings of the National Academy of Sciences of the United States of America, 109(48), 19703–19708. Retrieved from this resource:

Geller, L. (2001). Under the weather: Climate, ecosystems, and infectious disease. Emerging Infectious Diseases, 7(7), 606–608.Find this resource:

Germ Theory. (n.d.). Science Museum’s History of Medicine website, Brought to life, Techniques & Technologies, Germ Theory. Retrieved from

Gibbons, C. L., Mangen, M.-J. J., Plass, D., Havelaar, A. H., Brooke, R. J., Kramarz, P., … Kretzschmar, M. E. E. (2014). Measuring underreporting and under-ascertainment in infectious disease datasets: A comparison of methods. BMC Public Health, 14(1), 147.Find this resource:

Gilbert, L., Aungier, J., & Tomkins, J. L. (2014). Climate of origin affects tick (Ixodes ricinus) host-seeking behavior in response to temperature: Implications for resilience to climate change?Ecology and Evolution, 4(7), 1186–1198.Find this resource:

Gjenero-Margan, I., Aleraj, B., Krajcar, D., Lesnikar, V., Klobučar, A., Pem-Novosel, I., … Mlinarić-Galinović, G. (2011). Autochthonous dengue fever in Croatia, August–September 2010. Euro Surveillance : Bulletin Européen Sur Les Maladies Transmissibles = European Communicable Disease Bulletin, 16(9), 1–4.Find this resource:

Gorman, M. E., Kincannon, A., & Mehalik, M. M. (2001). Spherical horses and shared toothbrushes: Lessons learned from a workshop on scientific and technological thinking. Berlin: Springer.Find this resource:

Grad, Y. H., & Lipsitch, M. (2014). Epidemiologic data and pathogen genome sequences: A powerful synergy for public health. Genome Biology, 15(11), 538.Find this resource:

Grant, C., Lo Iacono, G., Dzingirai, V., Bett, B., Winnebah, T. R. A., & Atkinson, P. M. (2016). Moving interdisciplinary science forward: Integrating participatory modelling with mathematical modelling of zoonotic disease in Africa. Infectious Diseases of Poverty, 5(1), 17.Find this resource:

Grimshaw, R. (1993). Nonlinear ordinary differential equations. Ann Arbor, MI: CRC Press.Find this resource:

Halliday, S. (2001). Death and miasma in Victorian London: An obstinate belief. British Medical Journal, 323(7327), 1469–1471.Find this resource:

Heesterbeek, J. A. P., & Roberts, M. G. (2015). How mathematical epidemiology became a field of biology: A commentary on Anderson and May (1981). “The population dynamics of microparasites and their invertebrate hosts”. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 370(1666), 20140307.Find this resource:

Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4), 599–653.Find this resource:

Hippocrates. (1868). Hippocrates.pdf. In W. H. S. Jones (Ed.), Hippocrates collected works I. Cambridge, MA: Harvard University Press. Retrieved from this resource:

Hoffmann, A. A., & Sgrò, C. M. (2011). Climate change and evolutionary adaptation. Nature, 470(7335), 479–485.Find this resource:

Hoffmann, A. A., & Willi, Y. (2008). Detecting genetic responses to environmental change. Nature Reviews Genetics, 9(6), 421–432.Find this resource:

Howard-Jones, N. (1984). Robert Koch and the cholera vibrio: A centenary. British Medical Journal (Clinical Research Ed.), 288(6414), 379–381.Find this resource:

Jacob, C. (2010). Branching processes: Their role in epidemiology. International Journal of Environmental Research and Public Health, 7(3), 1186–1204.Find this resource:

Johnson, D. L., Ambrose, S. H., Bassett, T. J., Bowen, M. L., Crummey, D. E., Isaacson, J. S., … Winter-Nelson, A. E. (1997). Meanings of environmental terms. Journal of Environment Quality, 26(3), 581.Find this resource:

Johnson, P. T. J., Ostfeld, R. S., & Keesing, F. (2015). Frontiers in research on biodiversity and disease. Ecology Letters, 18(10), 1119–1133.Find this resource:

Jones, K. E., Patel, N. G., Levy, M. A., Storeygard, A., Balk, D., Gittleman, J. L., & Daszak, P. (2008). Global trends in emerging infectious diseases. Nature, 451(7181), 990–993.Find this resource:

Karamanou, M., Panayiotakopoulos, G., Tsoucalas, G., Kousoulis, A. A., & Androutsos, G. (2012). From miasmas to germs: A historical approach to theories of infectious disease transmission. LSHTM Research Online, 20(1), 52–56.Find this resource:

Keeling, M. J. (1999). The effects of local spatial structure on epidemiological invasions. Proceedings of the Royal Society B: Biological Sciences, 266(1421), 859–867.Find this resource:

Keeling, M. J., & Rohani, P. (2008). Modeling infectious diseases in humans and animals. Clinical Infectious Diseases (Vol. 47). Princeton, NJ: Princeton University Press. Retrieved from this resource:

Keeling, M. J., & Ross, J. V. (2008). On methods for studying stochastic disease dynamics. Journal of the Royal Society Interface, 5(19), 171–181.Find this resource:

Keesing, F., Belden, L. K., Daszak, P., Dobson, A., Harvell, C. D., Holt, R. D., … Ostfeld, R. S. (2010). Impacts of biodiversity on the emergence and transmission of infectious diseases. Nature, 468(7324), 647–652.Find this resource:

Kermack, W. O., & McKendrick, a. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 115(772), 700–721.Find this resource:

Klausmeier, C. A. (2008). Floquet theory: A useful tool for understanding nonequilibrium dynamics. Theoretical Ecology, 1(3), 153–161.Find this resource:

Knülle, W., & Rudolph, D. (1982). Humidity relationships and water balance of ticks. In Physiology of Ticks (pp. 43–70). Oxford: Pergamon Press Ltd, Elsevier.Find this resource:

Koelle, K., Pascual, M., & Yunus, M. (2005). Pathogen adaptation to seasonal forcing and climate change. Proceedings of the Royal Society B: Biological Sciences, 272(1566), 971–977. Retrieved from this resource:

Koenraadt, C. J., Balenghien, T., Carpenter, S., Ducheyne, E., Elbers, A. R., Fife, M., … Seelig, F. (2014). Bluetongue, Schmallenberg—what is next? Culicoides-borne viral diseases in the 21st Century. BMC Veterinary Research, 10(1), 77.Find this resource:

Kubiak, R. J., Arinaminpathy, N., & McLean, A. R. (2010). Insights into the evolution and emergence of a novel infectious disease. PLoS Computational Biology, 6(9).Find this resource:

Kucharski, A., Mills, H., Pinsent, A., Fraser, C., Kerkhove, M. Van, & Donnelly, C. A. (2014). Distinguishing between reservoir exposure and human-to-human transmission for emerging pathogens using case onset data. PLoS Currents Outbreaks. March 7, Edition 1, 1–21.Find this resource:

Kurtenbach, K., Hanincová, K., Tsao, J. I., Margos, G., Fish, D., & Ogden, N. H. (2006). Fundamental processes in the evolutionary ecology of Lyme borreliosis. Nature Reviews Microbiology, 4(9), 660–669.Find this resource:

La Ruche, G., Souarès, Y., Armengaud, A., Peloux-Petiot, F., Delaunay, P., Desprès, P., … Gastellu-Etchegorry, M. (2010). First two autochthonous dengue virus infections in metropolitan France, September 2010. Eurosurveillance, 15(39), 1–5.Find this resource:

Lacroix, C., Jolles, A., Seabloom, E. W., Power, A. G., Mitchell, C. E., & Borer, E. T. (2014). Non-random biodiversity loss underlies predictable increases in viral disease prevalence. Journal of the Royal Society, Interface/the Royal Society, 11(92), 20130947.Find this resource:

Langmuir, A. D. (1961). Epidemiology of airborne infection. Bacteriological Reviews, 25, 173–181.Find this resource:

Lipp, E. K., Huq, A., & Colwell, R. R. (2002). Effects of global climate on infectious disease: The cholera model effects of global climate on infectious disease: The cholera model. Clinical Microbiology Reviews, 15(4), 757–770.Find this resource:

Lloyd-Smith, J. O., George, D., Pepin, K. M., Pitzer, V. E., Pulliam, J. R. C., Dobson, A. P., … Grenfell, B. T. (2009). Epidemic dynamics at the human-animal interface. Science (New York), 326(5958), 1362–1367.Find this resource:

Lo Iacono, G., Armstrong, B., Fleming, L. E., Elson, R., Kovats, S., Vardoulakis, S., & Nichols, G. L. (2017). Challenges in developing methods for quantifying the effects of weather and climate on water-associated diseases: A systematic review. PLOS Neglected Tropical Diseases, 11(6), e0005659.Find this resource:

Lo Iacono, G., Cunningham, A. A., Fichet-Calvet, E., Garry, R. F., Grant, D. S., Leach, M., … Wood, J. L. N. (2016). A unified framework for the infection dynamics of zoonotic spillover and spread. PLOS Neglected Tropical Diseases, 10(9), e0004957.Find this resource:

Lo Iacono, G., Robin, C. A., Newton, J. R., Gubbins, S., & Wood, J. L. N. (2013). Where are the horses? With the sheep or cows? Uncertain host location, vector-feeding preferences and the risk of African horse sickness transmission in Great Britain. Journal of the Royal Society Interface, 10(83), 20130194.Find this resource:

Lo Iacono, G., van den Bosch, F., & Gilligan, C. A. (2013). Durable resistance to crop pathogens: An epidemiological framework to predict risk under uncertainty. PLoS Computational Biology, 9(1), e1002870.Find this resource:

Lo Iacono, G., van den Bosch, F., & Paveley, N. (2012). The evolution of plant pathogens in response to host resistance: Factors affecting the gain from deployment of qualitative and quantitative resistance. Journal of Theoretical Biology, 304, 152–163.Find this resource:

Loeb, J., Goold, G. P., & Hooper, W. D. (1934). The Loeb classical library. No. 283: De Re Rustica. Cato & Varro. Cambridge, MA: Harvard University Press. Retrieved from this resource:

LoGiudice, K. (2003). The ecology of infectious disease: Effects of host diversity and community composition on Lyme disease risk. Proceedings of the …, 100(2), 567–571. Retrieved from this resource:

Ludwig, A., Ginsberg, H. S., Hickling, G. J., & Ogden, N. H. (2016). A dynamic population model to investigate effects of climate and climate-independent factors on the lifecycle of Amblyomma americanum (Acari: Ixodidae). Journal of Medical Entomology, 53(1), 99–115.Find this resource:

Macal, C. M., & North, M. J. (2010). Tutorial on agent-based modelling and simulation. Journal of Simulation, 4(3), 151–162.Find this resource:

Macpherson, C. N. L. (2005). Human behaviour and the epidemiology of parasitic zoonoses. International Journal for Parasitology, 35(11–12), 1319–1331.Find this resource:

Manlove, K. R., Walker, J. G., Craft, M. E., Huyvaert, K. P., Joseph, M. B., Miller, R. S., … Cross, P. C. (2016). “One health” or three? Publication silos among the one health disciplines. PLOS Biology, 14(4), e1002448.Find this resource:

Mari, L., Bertuzzo, E., Righetto, L., Casagrandi, R., Gatto, M., Rodriguez-Iturbe, I., & Rinaldo, A. (2012). On the role of human mobility in the spread of cholera epidemics: Towards an epidemiological movement ecology. Ecohydrology, 5(5), 531–540.Find this resource:

Marinović, A. B., Swaan, C., van Steenbergen, J., & Kretzschmar, M. (2015). Quantifying reporting timeliness to improve outbreak control. Emerging Infectious Diseases, 21(2), 209–216.Find this resource:

May, R. M. (2001). Stability and complexity in model ecosystems (2d ed.). Princeton, NJ: Princeton University Press.Find this resource:

Medlock, J. M., Hansford, K. M., Schaffner, F., Versteirt, V., Hendrickx, G., Zeller, H., & Bortel, W. Van. (2012). A review of the invasive mosquitoes in Europe: Ecology, public health risks, and control option. Vector-Borne and Zoonotic Diseases, 12(6), 435–447.Find this resource:

Moritz, C., & Agudo, R. (2013). The future of species under climate change: Resilience or decline?. Science, 341(6145), 504–508.Find this resource:

Morse, S. S. (1995). Factors in the emergence of infectious disease. Emerging Infectious Diseases, 1(1), 7–15.Find this resource:

Murray, J. (2002). Mathematical biology I: An introduction (3d ed., Vol. 79). Berlin: Springer-Verlag. Retrieved from this resource:

Nevill, E. M. (1978). The use of cattle to protect sheep from bluetongue infection. Journal of the South African Veterinary Association, 49(2), 129–130.Find this resource:

Nichols, G. L., Andersson, Y., Lindgren, E., Devaux, I., & Semenza, J. C. (2014). European monitoring systems and data for assessing environmental and climate impacts on human infectious diseases. International Journal of Environmental Research and Public Health, 11(4), 3894–3936.Find this resource:

Nichols, G. L., Richardson, J. F., Sheppard, S. K., Lane, C., & Sarran, C. (2012). Campylobacter epidemiology: A descriptive study reviewing 1 million cases in England and Wales between 1989 and 2011. BMJ Open, 2(4), 1–14.Find this resource:

Nutton, V. (1983). The seeds of disease: An explanation of contagion and infection from the Greeks to the Renaissance. Medical History, 27(1), 1–34.Find this resource:

Ogden, N. H., Bigras-Poulin, M., O’Callaghan, C. J., Barker, I. K., Lindsay, L. R., Maarouf, A., … Charron, D. (2005). A dynamic population model to investigate effects of climate on geographic range and seasonality of the tick Ixodes scapularis. International Journal for Parasitology, 35(4), 375–389.Find this resource:

Oliver, J. H. (1989). Biology and systematics of ticks (Acari: Ixodida). Annual Review of Ecology and Systematics, 20(1), 397–430.Find this resource:

Ostfeld, R. S. (2013). A Candide response to Panglossian accusations by Randolph and Dobson: biodiversity buffers disease. Parasitology, 140(10), 1196–1198.Find this resource:

Ostfeld, R. S., & Brunner, J. L. (2015). Climate change and Ixodes tick-borne diseases of humans. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 370(1665), 20140051.Find this resource:

Otero, M., Schweigmann, N., & Solari, H. G. (2008). A stochastic spatial dynamical model for Aedes aegypti. Bulletin of Mathematical Biology, 70(5), 1297–1325.Find this resource:

Otero, M., Solari, H. G., & Schweigmann, N. (2006). A stochastic population dynamics model for Aedes aegypti: formulation and application to a city with temperate climate. Bulletin of Mathematical Biology, 68(8), 1945–1974.Find this resource:

Patz, J. A., Githeko, A. K., Mccarty, J. P., Hussein, S., & Confalonieri, U. (2003). Climate change and infectious diseases. In A. J. McMichael, D. H. Campbell-Lendrum, C. F. Corvalan, K. L. Ebi, A. K. Githeko, J. D. Scheraga, & A. Woodward (Eds.), Climate change and human health risk and responses (pp. 103–132). Geneva, Switzerland: World Health Organization. Retrieved from this resource:

Patz, J. A., Graczyk, T. K., Geller, N., & Vittor, A. Y. (2000). Effects of environmental change on emerging parasitic diseases. International Journal for Parasitology, 30(12–13), 1395–1405.Find this resource:

Porta, M. (2014). A dictionairy of epidemiology (6th ed.). S. Greenland, M. Hernan, I. dos Santos Silva, J. M. Last, & A. Buron (Eds.). Oxford: Oxford University Press.Find this resource:

Purse, B. V, Carpenter, S., Venter, G. J., Bellis, G., & Mullens, B. A. (2015). Bionomics of temperate and tropical culicoides midges: Knowledge gaps and consequences for transmission of culicoides-borne viruses. Annual Review of Entomology, 60, 373–92.Find this resource:

Rabinowitz, P. M., Kock, R., Kachani, M., Kunkel, R., Thomas, J., Gilbert, J., … Rubin, C. (2013). Toward proof of concept of a one health approach to disease prediction and control. Emerging Infectious Diseases [Internet], 19(12).Find this resource:

Randolph, S. E., & Dobson, A. D. M. (2012). Pangloss revisited: A critique of the dilution effect and the biodiversity-buffers-disease paradigm. Parasitology, 139(7), 847–863.Find this resource:

Randolph, S. E., & Dobson, A. D. M. (2013). Commentary on “A Candide response to Panglossian accusations by Randolph and Dobson: Biodiversity buffers disease” by Dr. R. Ostfeld. Parasitology, 140(10), 1199–1200.Find this resource:

Randolph, S. E., Green, R. M., Hoodless, A. N., & Peacey, M. F. (2002). An empirical quantitative framework for the seasonal population dynamics of the tick Ixodes ricinus. International Journal for Parasitology, 32(8), 979–989.Find this resource:

Reeves, W. C., Hardy, J. L., Reisen, W. K., & Milby, M. M. (1994). Potential effect of global warming on mosquito-borne arboviruses. Journal of Medical Entomology, 31(3), 323–332.Find this resource:

Reisen, W. K., Fang, Y., & Martinez, V. M. (2006). Effects of temperature on the transmission of West Nile virus by Culex tarsalis (Diptera: Culicidae). Journal of Medical Entomology, 43(2), 309–317. Retrieved from this resource:

Reluga, T. C., & Shim, E. (2014). Population viscosity suppresses disease emergence by preserving local herd immunity. Proceedings of the Royal Society of London B: Biological Sciences, 281(1796), 20141901.Find this resource:

Restif, O., Hayman, D., Pulliam, J., Plowright, R., George, D., Bowen, R., … Mill, J. (2012). Model-guided fieldwork : An integrative framework for wildlife infectious disease research. Ecological Letters, 15, 1083–1094.Find this resource:

Rezza, G., Nicoletti, L., Angelini, R., Romi, R., Finarelli, A., Panning, M., … Cassone, A. (2007). Infection with chikungunya virus in Italy: An outbreak in a temperate region. The Lancet, 370(9602), 1840–1846.Find this resource:

Righetto, L., Bertuzzo, E., Mari, L., Schild, E., Casagrandi, R., Gatto, M., … Rinaldo, A. (2013). Rainfall mediations in the spreading of epidemic cholera. Advances in Water Resources, 60, 34–46.Find this resource:

Righetto, L., Casagrandi, R., Bertuzzo, E., Mari, L., Gatto, M., Rodriguez-Iturbe, I., & Rinaldo, A. (2012). The role of aquatic reservoir fluctuations in long-term cholera patterns. Epidemics, 4(1), 33–42. Retrieved from this resource:

Rogers, D. J., & Randolph, S. E. (2006). Climate change and vector-borne disease. Advances in Parasitology, 62(5), 345–381.Find this resource:

Rueda, L. M., Patel, K. J., Axtell, R. C., & Stinner, R. E. (1990). Temperature-dependent development and survival rates of Culex quinquefasciatus and Aedes aegypti (Diptera: Culicidae). Journal of Medical Entomology, 27(5), 892–898. Retrieved from this resource:

Salkeld, D. J., Padgett, K. a, & Jones, J. H. (2013). A meta-analysis suggesting that the relationship between biodiversity and risk of zoonotic pathogen transmission is idiosyncratic. Ecology Letters, 16(5), 679–686.Find this resource:

Santini, A. (2015). Plant pathogen evolution and climate change. CAB Reviews: Perspectives in Agriculture, Veterinary Science, Nutrition and Natural Resources, 10(35), 1–8.Find this resource:

Sartwell, P. E. (1995). The distribution of incubation periods of infectious disease, 1949. American Journal of Epidemiology, 141(5), 386–394; discussion 385.Find this resource:

Satcher, D. (1995). Emerging infections: Getting ahead of the curve early history of infectious diseases. Emerging Infectious Diseases, 1(1), 1–6.Find this resource:

Schoolfield, R. M., Sharpe, P. J., & Magnuson, C. E. (1981). Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. Journal of Theoretical Biology, 88(4), 719–731. Retrieved from this resource:

Scoones, I., Jones, K., Lo Iacono, G., Redding, D., Wilkinson, A., & Wood, J. L. N. (2017). Integrative modelling for One Health: Pattern, process and participation. Philosophical Transactions of the Royal Society B: Biological Sciences, 372, 20160164Find this resource:

Shaffer, J. G., Grant, D. S., Schieffelin, J. S., Boisen, M. L., Goba, A., Hartnett, J. N., … Garry, R. F. (2014). Lassa fever in post-conflict Sierra Leone. PLoS Neglected Tropical Diseases, 8(3), e2748.Find this resource:

Shaman, J., Spiegelman, M., Cane, M., & Stieglitz, M. (2006). A hydrologically driven model of swamp water mosquito population dynamics. Ecological Modelling, 194(4), 395–404.Find this resource:

Sharpe, P. J., & DeMichele, D. W. (1977). Reaction kinetics of poikilotherm development. Journal of Theoretical Biology, 64(4), 649–670. Retrieved from this resource:

Slingenbergh, J. I., Gilbert, M., de Balogh, K. I., & Wint, W. (2004). Ecological sources of zoonotic diseases. Revue Scientifique et Technique (International Office of Epizootics), 23(2), 467–484. Retrieved from this resource:

Smith, D. L., Battle, K. E., Hay, S. I., Barker, C. M., Scott, T. W., & McKenzie, F. E. (2012). Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathogens, 8(4), e1002588.Find this resource:

Soti, V., Chevalier, V., Maura, J., Bégué, A., Lelong, C., Lancelot, R., … Tran, A. (2013). Identifying landscape features associated with Rift Valley fever virus transmission, Ferlo region, Senegal, using very high spatial resolution satellite imagery. International Journal of Health Geographics, 12, 10.Find this resource:

Soti, V., Tran, A., Degenne, P., Chevalier, V., Lo Seen, D., Thiongane, Y., … Fontenille, D. (2012). Combining hydrology and mosquito population models to identify the drivers of Rift Valley fever emergence in semi-arid regions of West Africa. PLoS Neglected Tropical Diseases, 6(8), e1795.Find this resource:

Stathakou, N. P., Stathakou, G. P., Damianaki, S. G., Toumbis-Ioannou, E., & Stavrianeas, N. G. (2009). The bio-medical comments of Empedocles A precursor to modern science. Archives of Hellenic Medicine, 26(2), 262–265.Find this resource:

Thrall, P. H., Oakeshott, J. G., Fitt, G., Southerton, S., Burdon, J. J., Sheppard, A., … Ford Denison, R. (2011). Evolution in agriculture: the application of evolutionary approaches to the management of biotic interactions in agro-ecosystems. Evolutionary Applications, 4(2), 200–215.Find this resource:

Thucydides. (1933). History of the Peloponnesian War. Trans. Richard Crawley) (reprinted in 1933). London: J. M. Dent & Sons.Find this resource:

Tomasello, D., & Schlagenhauf, P. (2013). Chikungunya and dengue autochthonous cases in Europe, 2007–2012. Travel Medicine and Infectious Disease, 11(5), 274–284.Find this resource:

Torres Codeco, C. (2001). Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir. BMC Infectious Diseases, 1(1). Retrieved from this resource:

Tuljapurkar, S., & Caswell, H. (Eds.). (1997). Structured-population models in marine, terrestrial, and freshwater systems. Structured-population models in marine, terrestrial, and freshwater systems. Boston: Springer. Retrieved from this resource:

Turell, M. J. (1989). Effect of environmental temperature on the vector competence of Aedes fowleri for rift valley fever virus. Research in Virology 140(2), 147–154.Find this resource:

Verelst, F., Willem, L., & Beutels, P. (2016). Behavioural change models for infectious disease transmission : a systematic review (2010–2015). Journal of the Royal Society Interface, 13(125), 20160820.Find this resource:

Walther, G. R., Post, E., Convey, P., Menzel, A., Parmesan, C., Beebee, T. J. C., … Bairlein, F. (2002). Ecological responses to recent climate change. Nature, 416(6879), 389–395.Find this resource:

Webb, P. A, McCormick, J. B., King, I. J., Bosman, I., Johnson, K. M., Elliott, L. H., … O’Sullivan, R. (1986). Lassa fever in children in Sierra Leone, West Africa. Transactions of the Royal Society of Tropical Medicine and Hygiene, 80(4), 577–582. Retrieved from this resource:

Whitmee, S., Haines, A., Beyrer, C., Boltz, F., Capon, A. G., de Souza Dias, B. F., … Yach, D. (2015). Safeguarding human health in the Anthropocene epoch: Report of The Rockefeller Foundation?. Lancet Commission on planetary health. The Lancet, 386(10007), 1973–2028.Find this resource:

Zinsstag, J., Mackenzie, J. S., Jeggo, M., Heymann, D. L., Patz, J. A., & Daszak, P. (2012). Mainstreaming one health. EcoHealth, 9(2), 107–110.Find this resource: