1) What are the main water-associated pathogens investigated and where do they occur?

Fig 3 shows the frequency of pathogens in the final set of papers. Vibrio cholerae has been studied most for climate and weather effects. A significant proportion (approximately 20% of papers) focused on unspecified water-associate pathogens and these studies were mostly theoretical process-based models. The next significant categories of studies were papers that looked at diarrheal illness as a broad category based on health service data that did not include pathogen-specific information. In terms of pathogen -specific outcomes, the following pathogens were most studied (after Vibrio cholerae): Cryptosporidium spp., Leptospira spp., Schistosoma spp. Giardia sp. and Salmonella spp. Many of these are classified as NTD [2–4] e.g. Vibrio cholerae, Leptospira spp., Schistosoma spp. Giardia sp. (Table 1).

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Fig 3. Proportion of papers investigating a particular pathogen or disease.

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Fig 4 shows the countries where the studies were based. A good proportion of these theoretical process-based models did not link their study with any data for diseases occurring in a particular country (therefore, the outcome was listed as “General” in Fig 4). The country with the most studies (about 10% of papers) was Bangladesh, mostly in relation to cholera, followed by studies on disease data collected in US, China and Canada (Fig 4).

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Fig 4. (a) Distribution of countries for which water-associated disease data were the focus of the reviewed papers (b) Geographic distribution of the 7 most commonly studied water-associated pathogens (resulting either in an epidemic or endemic situations) which were the focus of the reviewed papers.

Each circle refers to specific countries, In particular, the largest circle in Asia, refers to Bangladesh.

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Thus, the pathogens reported in these studies reflect geographic (origin of infections) and socio-economic (quality of data) features: studies on cholera were associated with low and middle income countries, while Cryptosporidium spp. and Campylobacter spp. were more likely reported in high income countries that have good laboratory-based passive surveillance systems (Fig 4).

2) What methods have been used?

The set of all technical keywords describing the methods used in at least two papers is displayed in a keyword network in Fig 5 (a high-resolution image for the methods used in each paper can be found in the Supporting Information, S1 Fig, see also S1 Table). The figure suggests that the most commonly used methods can be grouped into two main clusters:

• Process-Based Models (PBM), which are typically described by mechanistic compartmental models [14],
• Time series and spatial epidemiology (TS-SE) such as time series and regression analysis [15] and spatial methods typically based on geographic information system (GIS) [16].

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Fig 5. Cluster analysis of methods.

Each dot corresponds to a reviewed paper; the brown bubbles correspond to the keywords describing the techniques. A connection between a paper and a keyword occurs when the related technique is used. The size of the bubble increases (logarithmically) with the number of papers citing the keyword. For visual purpose only, i) the bubbles are displayed with different shades of brown and ii) the technical keywords (listed in S1 Table in the Supporting Information) describing methods used by only one paper are not displayed (the full set is shown in S1 Fig in the Supporting Information). The graph was produced by using the i-graph package[13] in R.

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These clusters can overlap. For examples, instances of spatial compartmental models have been developed.

Fig 5 is perhaps the most objective way of representing the methods used in the reviewed papers as it is based simply on the technical keywords recorded by their authors. As the technical keywords can be very specific, the next exercise was to identify the general methods used in the papers. A list of the most common general methods is shown in Fig 6 and in S1 Table in the Supporting Information. The entries in Fig 6 and S1 Table do not reflect an established”taxonomy” of the methods (which is not available in the literature); they are mainly guided by the patterns which emerged from keyword network (Fig 5) and selected based on their potential relevance for the study of the effects of weather and climate. For example, a close inspection of Fig 5 suggests that a substantial number of papers in the PBM clusters employed “Dose-Response Model” (which often use environmental variables, such as temperature as inputs); we therefore identified “Models comprising Exposure-Response Relantionship” as a general method.

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Fig 6. The most common, general methods used in the reviewed papers (listed in S1 Table in the supporting information).

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The same principle guided the structure of Table 3, which presents some key features of the clusters of methods. In Table 3, however, we did not discuss methods such as “Descriptive Statistics” and “Survey/Surveillance/Sampling” since these were too generic in terms of their use for investigating the effect of weather and/or climate change on water-associated diseases. Conversely, the table contains additional entries that did not emerge from the patterns from Fig 5, but we recognized that they are important for such use (e.g. “Investigation of seasonality” and separation of “Time Series Regression” in short and long term studies).

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Table 3. Discussion of some key features of the general methods and their relevance to the investigation of the effect of weather and/or climate change.

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Process-based methods (PBM). Most PBM are based on compartmental models, i.e. a subdivision of the entire population into relevant epidemiological categories, such as susceptible, infected, and recovered people [14]. The population dynamics of each category is usually governed by a system of non-linear differential equations (with each single equation corresponding to the rate of change of each compartment). This class of models has been extended to stochastic, spatial and age-specific models. The compartmental models in our Review included an additional compartment describing the dynamic of the pathogen population in the environment (e.g. the concentration of the pathogen in the water reservoir) which is then linked in some way to temperature and/or rainfall factors (e.g., rainfall affects the volume of the water reservoir, which determines the dilution of the pathogen and, thus, the probability of contracting the disease; temperature affects the growth and survival of many free living pathogens, such as E. coli, in the water reservoir). An infection occurs when a susceptible person comes in contact with this additional category. Infected people can excrete pathogens, and feedback into the environment compartment (included in the majority of the PBM-papers), although for some infections there is no excretion and thus no feedback into the environment (e.g. Legionella). Ten percent of PBM-papers also included person-to-person transmission via contacts between susceptible and infected persons. The cluster PBM also contained sub-clusters: “Exposure–Response Relationship”, “Stability Analysis”, “Human Mobility”, and “Network Analysis” (Fig 5). Important features of the clusters are discussed in Table 3.

Cluster TS-SE. Time series regression (TSR) analysis [15,17] is one of the most common methods used by the papers reviewed to analyse temperature and rainfall exposures as they can vary over time. Many studies used generalized linear models (GLMs) and generalized additive models (GAMs) often included terms allowing for over-dispersion. Terms to control for seasonality (time stratified model, Fourier terms, spline functions) and autocorrelation terms are often included. In most cases, residual variation in the response variable (e.g. daily counts of disease occurrence) was modelled as a Poisson distribution, followed by negative binomial. The most common exposure factors were temperature and rainfall. Socio-economic indicators were often included in the analysis.

As noted in the systematic review of Imai and Hashizume [15], only a few studies included variations in the susceptible population over time, due to, for instance, changes in immunity following disease recovery. Autoregressive models (e.g. ARMA, ARIMA, SARIMA, ARIMAX), which intrinsically take into account correlation, were used in some studies (Fig 6), although many studies in the regression tradition used ad hoc approaches for this. These methods were often used to investigate the temporal lag between the exposure and the response variable (e.g. daily counts of disease occurrence).

Spatial methods for linking datasets use geographical information systems (GIS) to link disease data with information on socio-economic indicators, temperature and rainfall (or proxy indicators), and vegetation and land use data within the same geographical framework. Geo-referenced environmental data can be collected by remote sensing [16,18] and ground-station data.

Other less commonly used analytical methods included wavelet analysis [19], and the social science approach of participatory modelling [20].

3) Is the method applied to investigate the effects of climate or weather?

Most of the reviewed papers (49% of the papers explicitly emphasized this application in the Abstract) investigated the effects of weather (i.e. short-term changes in the atmosphere, such as daily or weekly exposures to rainfall) on infectious disease. Only 9% of the reviewed papers applied the methodology to study the effects of climate, i.e. long-term averages of weather such as El Niño cycles (these applications are not mutually exclusive); and 7% used modelled future climate projections. Collinearity of exposures, i.e. highly correlated predictor variables in regression models, is an important limitation in weather and climate studies but was only explicitly identified as a limitation in 7% of studies).

4) Does the type of method depend on the disease/pathogen under investigation?

Approximately 50% of papers investigating Vibrio cholerae employed methods based on compartmental models, followed by time-series/regression analysis and spatial/GIS analysis using cholera case observations. Similar patterns were observed for unspecified water-associated pathogens. As expected, for generic diarrheal pathogens (for which there is much more uncertainty about the causes), spatial/GIS and time-series/regression analysis were the most commonly used methods (but see discussion in [1] and [21]).

5) Some key feature in the methods: e.g. What are the independent variables in the models? Does the model take into account seasonality?

More than 70% of studies included observed or modelled temperature and/or rainfall/precipitation data in their analysis. A smaller proportion of studies included (the inclusion is not mutually exclusive) other environmental factors (e.g., relative humidity, vapor air pressure, evaporation) and socio-economic indicators (e.g. access to water, index of poverty, age, education, human mobility) in the analysis (Fig 7).

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Fig 7. The most common environmental and socio-economic variables included in the reviewed papers.

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Around 40% of the methods explicitly included the effects of seasonality (intra-annual climate variability). A small proportion of papers (7%) included the effects of El Niño/Southern Oscillation (ENSO) and North Atlantic Oscillations (NAO). Almost 40% of the methods took into account spatial variation. Only a small proportion of the methods explicitly modelled the pathogen dynamics in the wider environment or the specific water reservoir; a proportion of these studies (typically, theoretical works for a proof of concept) developed general methods without focusing on specific environmental variables, but the method could be potentially applied to investigate their effects.

6) How were the results assessed?

The statistical methods used to fit a model with the observed data were assessed with information criteria (such as Akaike Information Criterion, AIC and Bayesian Information Criterion, BIC) in almost 20% of cases. In a significant proportion of papers (10%), the validation of the method was based on out-of-sample predictions, i.e. a subset of the data were used to train/calibrate the method (e.g. to estimate model parameters), and then the method was applied to the rest of the data. In some cases, there was no assessment of the methods. Situations where the methods did not require comparison with real data (e.g. theoretical works requiring solely logical demonstration of theorems) were also present.

7) What are the method limitations for analysing climate and weather effects identified by the authors?

The lack of inclusion of relevant factors in the methods was the most common limitation acknowledged by the authors. These included: spatial and socio-economic heterogeneity, seasonality, changing immunity, and other environmental drivers. In almost 20% of papers, the authors identified reporting bias as a key limitation. Examples of reporting bias were: sample collections not properly designed (e.g. not stratified by age); voluntary internet-based survey reflecting survey respondents’ idiosyncrasies; and health-seeking behaviours and socio-economic factors affecting access to health facilities.

The poor quality of the data was another important source of limitation according to the authors, and this was explicitly mentioned in around 30% of reviewed papers. Typical examples of poor data quality were: low spatio-temporal resolution of the exposure data (e.g. environmental exposure covered a wide geographic area or linked to a single weather stations); lack of longitudinal data (only cross-sectional surveys were undertaken); and low accuracy of the data (e.g. reliance on proxy data, missing data due to asymptomatic or unobserved infections).

In 10% of cases, the methods were not able to explain the observed patterns in the disease outcome. The authors identified the absence of underlying mechanistic explanation as a problem in about 10% of the studies. In 10% of papers, the authors highlighted that the methods were calibrated only for a specific situation (e.g. a limited region), and the findings were not generalizable.

1) Disentangling multiple transmission pathways and identifying the bio-physical mechanism of how weather affects disease and seasonality.

In general, the spread of many pathogens is subjected to concurrent modes of transmissions, as exemplified in Fig 1. For instance, cholera can be acquired from contamination of household water storage containers, food preparation, direct person-to-person contacts, and/or via contact with environmental reservoir with long pathogen persistence [22,23]. Identifying a potential signature for the particular pathways in the patterns of diseases is perhaps the ideal goal. In particular, to separate person-to-person transmission from other modes of disease transmissions a range of methods have been proposed, including nonlinear time series approaches linked with wavelet analysis [24] and mechanistic compartmental approaches [22,23]. Despite such efforts, isolating the contributions of person-to-person transmission on the burden of these diseases is a compelling problem not only for water-associated diseases but all infectious diseases [25,26].

Different transmission pathways can be strongly affected by weather and/or climate. For example, temperature may have direct effects on Salmonella bacterial proliferation at various stages in the food chain (including bacterial loads on raw food production, transport and inappropriate storage), and indirect effects on eating behaviours during hot days [27]. Rainfall might increase person-to-environment transmission of cholera, by facilitating the contamination of fresh water from the sewage system. Rainfall might also dilute the concentrations of the pathogens, reducing environment-to-person transmission [28]. Compartmental models have also been used to investigate the effects of pathogen dilution due to the seasonal variation of water volume (e.g. with monsoons) and the potential interactions with other environmental drivers (e.g. temperature [29,30] and the effects of human mobility) [31].

The key challenge ahead are increasing the awareness of the drivers of disease and a deeper integration with fields such as microbiology (e.g. identifying dose-response curves to use as input for modelling, potential coexistence of human-to-human transmission), social science (e.g. to identify and include in the methods social contacts, patterns of mobility, adaptation, etc.), and ecology (e.g. to understand and incorporate the dynamics of free living organisms in water).

2) Reducing uncertainty in reporting.

Measuring the ‘true’ incidence of disease, and therefore morbidity and mortality rates, is a common problem in epidemiology. This includes: the under-ascertainment arising when not all cases seek healthcare; under-reporting due to failure in the surveillance system; and reporting bias [32,33]. Community-based studies have been employed to reduce the uncertainty in reporting a range of diseases, including water-associated diseases [34]. These methods usually involve the acquisition of data, e.g. by questionnaire possibly accompanied by biological sampling (e.g. serological surveys), in a representative population such as a retrospective cohorts or a population cross-sections. These methods can be integrated with statistical and mathematical approaches to estimate incidence. For a review of these methods, see [34] and references therein.

A common problem with these methods is that they are sensitive to the particular situation under investigation, such as country, age and social group. In addition, the climate and/or weather can have a direct impact on reporting. For example, impassable roads reducing the ability to seek medical care, and therefore detection, during the rainy season might explain the apparent seasonality of incidence of Lassa fever in humans in Sierra Leone [35]. This last example underscores the importance of integrating a variety of approaches including not only serology, lab-based sampling and statistical/mathematical models, but also participatory modelling and ethnographic research [36] to assess perceptions of risk, approaches to hygiene, health-seeking behaviour and accessibility; and how economic and social factors affect the reliability of data collection by, or reporting to, the surveillance system [35–37].

3) Identifying the key risk factors/disease determinants and tackling collinearity.

A key task is often to detect the main risk factors or disease determinants, and quantify their impacts. A closely related problem is collinearity (also called multi-collinearity), i.e. the situation where two or more predictor variables in a statistical model are linearly related. Collinearity might generate numerical problems, i.e. instability of parameter estimates and inflated variance of the estimated regression coefficient. In particular, collinearity often makes it impossible to attribute the effects on the response variable to the individual predictor variables [38]. This is part of the wider epistemological problem of association vs. causation, which is not discussed here and we refer the interested reader to, for instance, the Bradford-Hill guidelines [39].

In our context, a common source of collinearity is the highly correlated climatic variables such as temperature and rainfall. In some cases, collinearity can have a limited impact on inference, if the correlation between variables remains unchanged [40]. Patterns of collinearity between climatic variables, however, strongly depend on geographic location and environment (e.g. eco-zones) [38]; and they might vary in time due to climate change. This prevents meaningful interpretation/extrapolation of the findings beyond the geographic or environmental range of sampled data.

We share the view of Dormann et al. [38] that without a mechanistic understanding of the biophysical process, collinear variables cannot be separated by statistical means alone. This requires an understanding of the relationships between the different predictor variables, e.g. the dependence of humidity on temperature and rainfall, e.g. [41], or between the response variable and one or more predictor variables, e.g. the dependence of Salmonella growth on temperature.

Such mechanistic insights are not always available and one must rely on solely statistical approaches. Under this scenario, Dormann et al. [38] conducted a systematic review of methods to deal with collinearity and a simulation study evaluating their performance (in absence of mechanistic understanding) with regard to robust model fitting and prediction.

The methodologies assessed in [38], for detecting and removing collinearities include clustering (e.g. Principal Component Analysis-based Clustering, Iterative Variance Inflation Factor Analysis), cluster-independent methods (e.g. Selection of Uncorrelated Variables, Sequential Regression), latent variable regressions (e.g. Principal Component Regression, Partial Least Squares, Dimension Reduction Techniques), and a range of approaches that may be less sensitive to collinearity (e.g. Penalised Regressions, Machine-Learning methods, Collinearity-Weighted Regression). Fourier analysis is another approach that, from each time series of predictors, extracts a set of orthogonal data to be used as new descriptor uncorrelated variables [18,42]. Bayesian Network Analysis is another promising tool to identify statistical dependencies between multiple variables, and to separate these into those directly and indirectly dependent with one or more response variables [43]. This data-driven statistical tool produces a graphical network, whose structure describes the interdependency between variables [43,44]. In contrast with Path Analysis [45], Bayesian network analysis does not assume any causal relationships although this can be introduced by appropriate prior distribution for the structure of the graphical network. In particular, the method has been applied to investigate socio-economic determinants for diarrheal diseases and the role of weather in animal diseases [43,46]. Another method, applied to the 1993 Milwaukee Cryptosporidium outbreak [47], integrates population dynamic models with Profile Likelihood approach [48]. The problem of collinearity is removed by fixing the value of one or more parameters, and then estimating the remaining ones by maximizing the (log-) likelihood of the associated model; the approach is then repeated for a range of values of the fixed parameters. The method, which is suitable for a limited subset of the parameters, provides a better understanding of the relationship among different parameters.

4) Identifying and quantifying the different sources of the temporal lag from the start of the pathway to infection to disease detection.

The effects of the different meteorological, climatic, environmental and socio-economic factors on occurrence of disease are not instantaneous. Fig 1 illustrates some of the complexity. Sources of the temporal lag include the time required for potential growth of pathogen population in the environment, exposure dynamics, incubation period, and delays in reporting.

Further complications can arise from feedback from the infected population to the pathogen reservoir (e.g. rainfall facilitating contamination of fresh water from the sewage system). The required time t_res, for the pathogen population in the reservoir to replicate and reach a sufficient value to cause infections, depends on a range of environmental and microbiological factors specific to the pathogen under investigation. Methods to estimate this time and its distribution are beyond the scope of this Review; here we simple mention some mechanistic approaches and a separate published review for temperature-driven bacterial growth in food and in water drinking systems [49–53]. The required time t_exp, for susceptible individuals to be infected after being exposed to the pathogen reservoir, depends on the particular route of transmission and type of exposure.

The literature on microbial risk assessment framework (hazard identification, dose-response relationships, exposure assessment, quantitative risk characterization) represents an important source of methods to estimate the probability of infection and disease resulting from exposure to a variety of pathogenic microorganisms [54–56]. The effect of exposure events is, in general, distributed over a time interval. A range of approaches, based on time series analysis, has been implemented to study the distributed effects of multiple episodes of exposure on infectious outbreaks (see [57] and references therein). A general statistical framework that can simultaneously represent non-linear exposure–response dependencies (due to, for example, depletion of susceptibles) and delayed effects has been recently formulated [58].

Infections are typically revealed after the incubation period, t_inc, (the time between infections and symptoms onsets); which is associated with patient’s physiology, whose distribution depends on the type of infection (see historical paper of Sartwell [59]). After symptoms start, only a proportion of the infected individuals seeks medical assistance (see issue above on reporting), and for only a proportion of these cases further diagnostic testing will be conducted and recorded in the public health system. This introduces a further time lag, t_det, between the time when infected individual approaches the health system and the actual appropriate laboratory detection with diagnosis [60,61]. Even in a simple scenario, the temporal lag between the start of the pathway to infection (which can be challenging to define) and disease detection is a combination the time lags t_res, t_exp, t_inc, t_det. These are typically represented by random variables drawn from adequate distributions; for example a log-normal distribution has been proposed for t_inc and t_det.

Key challenges include: these distributions are expected to be dependent on a range of factors (patient’s physiology, environment, reporting bias), they are not necessarily stationary [61], and the technical difficulties inherent with the algebra of random variables [62]. Estimating the time lag between environmental/climatic variables and infections was a common task encountered in this Review, however, none of the methods used distinguished the different sources of time lag, and in most cases the assessment was based on trial and error methods (typically, searching for high correlation between the time series of incidence and the time series of temperature and/or rainfall at 1,2, etc. weeks before the date of reported case) followed by some significance tests or selection criteria (e.g. p-values, AIC [63]).

Involving the wider community via community-based studies and citizen science could help in identifying the different sources of the temporal lag from the start of the pathway to infection to disease detection. This information could be used as inputs for agent based models (ABM) to simulate controlled processes in epidemics, and to assess the capability of these models to identify the multiple sources (physiology, environment, behaviour) of time lags and their statistical distributions.

5) Studying the evolution of pathogen in response to climate change/variability.

Very little research has investigated the potential effect of observed climate change/variability on the evolution and adaptation of pathogens [56], that is changes in the climate (e.g. mean temperature and rainfall, patterns of seasonality, etc.) on over decadal time scales. In particular, seasonality is expected to be an important driver of pathogen evolution (see [64–66] and references therein), as periods of high transmission are followed by population bottlenecks reducing strain diversity and causing rapid genetic shifts. Furthermore, external periodic perturbations (e.g. seasonality in temperature, rainfall) can resonate with the natural frequencies of the ecosystem, promoting emergency or suppression of particular strains of the pathogen [66]. Apart from the theoretical work of Koelle et al [67] which might explain the cholera strain replacement in Bangladesh due to changes in monsoon rainfall patterns, we are not aware of further research investigating evolution of water-associated pathogens in response to climate change.

6) Investigating the effects of time-varying factors on transmission patterns.

The importance of and challenges in understanding the effects of seasonal drivers and climate variability on the dynamics of infectious diseases are largely recognized [24,64,68–71] and not repeated here. Further challenges arise from potential changes in seasonal patterns of the drivers, for example due to control measures, and aperiodic time-varying factors [72]. Stability analysis for seasonal systems, i.e. studying the conditions for pathogen invasion and establishment in systems characterized by fluctuating environmental forcing (based for example on Floquet analysis [30,73]), represents an interesting area for future research.

7) Dealing with different spatio-temporal scales.

The mechanistic approaches reviewed here were in most cases deterministic compartmental models, which are strictly only valid for large epidemics. Water-associated disease outbreaks could be point-source, affecting a relatively small population. For this situation, stochastic process-based models coupled with local weather and environmental variables could be beneficial. Quantitative methodological studies applied to longer term climatic effects are limited. Extreme events, such as prolonged droughts (months or years) and heavy rain events (days or weeks), are expected to have a major impact on the dynamics of infectious diseases [74–77]. The papers reviewed here focused on the intensity of the events alone, not their frequency. Furthermore, there is no consensus on the definition of extreme weather events [77].

None of the reviewed paper investigated the long term effect of human adaptation to climatic change. The effects of Earth atmosphere range from short term weather events, to intermediate time periods events like ENSO, to longer term climate change. We are not aware of any unified approach linking together the effects of the different time-scales on water-associated infectious diseases and their spatial distribution. Spatial analysis was often performed on a temporal snapshot (cross sectional study), usually to find correlation among different variables on different locations. Only a small proportion of spatial studies included temporal dynamics, for example to study the spread of cholera in a particular region due to rainfall. Longer term changes, such as land use changes, were rarely incorporated.

Tackling the many challenges.

Important data and theoretical challenges emerged with implications for the surveillance and control of water-associated infections. The inter-connections between human health, the environment, and also animal health as advocated by the One Health holistic vision [82], are increasingly recognized. Being aware of these connections and the potential bio-physical mechanisms occurring at different spatio-temporal scales is crucial to separate out the multiple transmission pathways, to understand and quantify the different sources of the temporal lag, and to deal with collinearity. Incorporating information on human behaviour and socio-economic factors can help to reduce reporting bias, and improve understanding of the potential effect on infectious diseases of anthropogenic climate change and interventions.

Collecting and linking long term, high-resolution, epidemiological, socio-economic, environmental and climatic data.

The integration of infection data with long-term, national-scale, environmental and land use data is an important growing approach [83]. For example, the national communicable diseases database of Public Health England has collected data from microbiology diagnostic laboratories (as well as patient’s addresses in the last five years) for England and Wales since 1989. The location of the diagnostic laboratories, or the patient residences, could be used to link cases to local weather parameters supplied by the UK Met Office in a confidential manner. These cases could also be linked with the spatial density of livestock data. The utility of these datasets could be further improved, as most current datasets are one-off surveys. Data on the spatio-temporal infection prevalence in livestock are also important information.

The paucity of this kind of information is much more pronounced for data on wildlife; with the exception of voluntary based schemes (such as citizen science [84]), we are not aware of a systematic collection of such data. Involving the wider public via community-based studies and citizen science could help in reducing the uncertainty in reporting and in identifying the different sources of the temporal lag from the start of the pathway to infection to disease detection. For example, surveys could be used by public health institutions to gather data on patient behaviour, symptom onset, food and water exposures, the likelihood of seeking medical advice, and the location of the potential sources of infection, etc.

Integrating bio-physical and socio-economic mechanisms of infectious disease.

The emergence, risk, spread, and control of infectious diseases are affected by many complex bio-physical, environmental and socio-economic factors [1]. These include climate and environmental change, land-use variation, and changes in population and human behaviour. For example, the abundance of long term, high-resolution, surveillance data (e.g. reported infectious diseases from Public Health England) linked with local weather parameters allows the analysis of the subset of epidemiological cases when all environmental variables (except one predictor, referred to as ‘test variable’) are fixed; in this way, the problem of collinearity is naturally removed. This exercise provides a family of curves of the rates of infection, which are function of the test variable and conditioned to all other fixed predictors. From the family of curves, the potential relationship between the predictors and the rate of infection can be inferred and potentially elucidate the bio-physical mechanism.

Conversely, functional relationships between epidemiological measures (e.g. incidence) and weather parameters arising from process-based models could be used as inputs for statistical models (e.g. by providing a particular relationship for the link function in a GLM). Feedbacks from community-based studies on human behaviour could also be integrated with process-based and statistical methods to design more realistic mathematical models, which in turn can assist with making policy decisions [35].