Seasonality and the dynamics of infectious diseases

Seasonality of infectious diseases

Seasonality, a periodic surge in disease incidence corresponding to seasons or other calendar periods, characterizes many infectious diseases of public health importance. The recognition of seasonal patterns in infectious disease occurrence dates back at least as far as the Hippocratic era, but mechanisms underlying seasonality of person-to-person transmitted diseases are not well understood. Improved understanding will enhance understanding of host-pathogen interactions and will improve the accuracy of public health surveillance and forecasting systems. Insight into seasonal disease patterns may be gained through the use of autocorrelation methods or construction of periodograms, while seasonal oscillation of infectious diseases can be easily simulated using simple transmission models. Models demonstrate that small seasonal changes in host or pathogen factors may be sufficient to create large seasonal surges in disease incidence, which may be important particularly in the context of global climate change. Seasonality represents a rich area for future research.

Worms and germs: the population dynamic consequences of microparasite-macroparasite co-infection

Hosts are typically simultaneously co-infected by a variety of microparasites (e.g. viruses and bacteria) and macroparasites (e.g. parasitic helminths). However, the population dynamical consequences of such co-infections and the implications for the effectiveness of imposed control programmes have yet to be fully realised. Mathematical models may provide an important framework for exploring such issues and have proved invaluable in helping to understand the factors affecting the epidemiology of single parasitic infections. Here the first population dynamic model of microparasite-macroparasite co-infection is presented and used to explore how co-infection alters the predictions of the existing single-species models. It is shown that incorporating an additional parasite species into existing models can greatly stabilise them, due to the combined density-dependent impacts on the host population, but co-infection can also restrict the region of parameter space where each species could persist alone. Overall it is concluded that the dynamic feedback between host, microparasite and macroparasite means that it is difficult to appreciate the factors affecting parasite persistence and predict the effectiveness of control by just studying one component in isolation.

Growth rate and basic reproduction number for population models with a simple periodic factor

For continuous-time population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions. As an example, we reconsider an SEIS model with a fixed latent period, an exponentially distributed infectious period and a sinusoidal contact rate studied in Williams and Dye [B.G. Williams, C. Dye, Infectious disease persistence when transmission varies seasonally, Math. Biosci. 145 (1997) 77]. We show that apart from a few exceptional parameter values, the epidemic threshold depends not only on the mean contact rate, but also on the amplitude of fluctuations.

Disease effects on reproduction can cause population cycles in seasonal environments

Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share the same host, and evidence is beginning to accumulate showing nonindependent effects of different infections.

We investigated the consequences for host population dynamics of a disease-induced period of no reproduction, and a chronic reduction in fecundity following recovery from infection (such as may be induced by secondary infections) using a modified SIR (susceptible, infected, recovered) model. We also included a seasonally varying birth rate as recent studies have demonstrated that seasonally varying parameters can have important effects on long-term host–parasite dynamics. We investigated the model predictions using parameters derived from five different cyclic rodent populations.

Delayed and reduced fecundity following recovery from infection have no effect on the ability of the disease to regulate the host population in the model as they have no effect on the basic reproductive rate. However, these factors can influence the long-term dynamics including whether or not they exhibit multiyear cycles.

The model predicts disease-induced multiyear cycles for a wide range of realistic parameter values. Host populations that recover relatively slowly following a disease-induced population crash are more likely to show multiyear cycles. Diseases for which the period of infection is brief, but full recovery of reproductive function is relatively slow, could generate large amplitude multiyear cycles of several years in length. Chronically reduced fecundity following recovery can also induce multiyear cycles, in support of previous theoretical studies.

When parameterized for cowpox virus in the cyclic field vole populations (Microtus agrestis) of Kielder Forest (northern England), the model predicts that the disease must chronically reduce host fecundity by more than 70%, following recovery from infection, for it to induce multiyear cycles. When the model predicts quasi-periodic multiyear cycles it also predicts that seroprevalence and the effective date of onset of the reproductive season are delayed density-dependent, two phenomena that have been recorded in the field.

Impact of myxomatosis in relation to local persistence in wild rabbit populations: the role of waning immunity and the reproductive period

Many diseases are less severe when they are contracted in early life. For highly lethal diseases, such as myxomatosis in rabbits, getting infected early in life can represent the best chance for an individual to survive the disease. For myxomatosis, early infections are attenuated by maternal antibodies. This may lead to the immunisation of the host, preventing the subsequent development of the lethal form of the disease. But early infection of young individuals requires specific demographic and epidemiological contexts, such as a high transmission rate of the pathogen agent. To investigate other factors involved in the impact of such diseases, we have built a stochastic model of a rabbit metapopulation infected by myxomatosis. We show that the impact of the pathogen agent can be reduced by early infections only when the agent has a long local persistence time and/or when the host subpopulations are highly connected. The length of the reproductive period and the duration of acquired immunity are also important factors influencing the persistence of the pathogen and thus, the impact of the disease. Besides confirming the role of classical factors in the persistence of a pathogen agent, such as the size of the subpopulation or the degree of connectivity, our results highlight novel factors that can modulate the impact of diseases whose severity increase with age.

Comparing models for early warning systems of neglected tropical diseases

Background

Early warning systems (EWS) are management tools to predict the occurrence of epidemics of infectious diseases. While climate-based EWS have been developed for malaria, no standard protocol to evaluate and compare EWS has been proposed. Additionally, there are several neglected tropical diseases whose transmission is sensitive to environmental conditions, for which no EWS have been proposed, though they represent a large burden for the affected populations.

Methodology/Principal Findings

In the present paper, an overview of the available linear and non-linear tools to predict seasonal time series of diseases is presented. Also, a general methodology to compare and evaluate models for prediction is presented and illustrated using American cutaneous leishmaniasis, a neglected tropical disease, as an example. The comparison of the different models using the predictive R² for forecasts of “out-of-fit” data (data that has not been used to fit the models) shows that for the several linear and non-linear models tested, the best results were obtained for seasonal autoregressive (SAR) models that incorporate climatic covariates. An additional bootstrapping experiment shows that the relationship of the disease time series with the climatic covariates is strong and consistent for the SAR modeling approach. While the autoregressive part of the model is not significant, the exogenous forcing due to climate is always statistically significant. Prediction accuracy can vary from 50% to over 80% for disease burden at time scales of one year or shorter.

Conclusions/Significance

This study illustrates a protocol for the development of EWS that includes three main steps: (i) the fitting of different models using several methodologies, (ii) the comparison of models based on the predictability of “out-of-fit” data, and (iii) the assessment of the robustness of the relationship between the disease and the variables in the model selected as best with an objective criterion.

Early Warning Systems (EWS) are management tools to predict the occurrence of epidemics. They are based on the dependence of a given infectious disease on environmental variables. Although several neglected tropical diseases are sensitive to the effect of climate, our ability to predict their dynamics has been barely studied. In this paper, we use several models to determine if the relationship between cases and climatic variability is robust—that is, not simply an artifact of model choice. We propose that EWS should be based on results from several models that are to be compared in terms of their ability to predict future number of cases. We use a specific metric for this comparison known as the predictive R², which measures the accuracy of the predictions. For example, an R² of 1 indicates perfect accuracy for predictions that perfectly match observed cases. For cutaneous leishmaniasis, R² values range from 72% to77%, well above predictions using mean seasonal values (64%). We emphasize that predictability should be evaluated with observations that have not been used to fit the model. Finally, we argue that EWS should incorporate climatic variables that are known to have a consistent relationship with the number of observed cases.

Epidemiology of a Daphnia brood parasite and its implications on host life-history traits

Parasites influence host life-history traits and therefore might crucially shape host populations in natural systems. In a series of laboratory experiments, we studied the impact of an oomycete brood parasite on its Daphnia (waterflea) host. We asked whether Daphnia dump the infected brood and subsequently are able to reproduce again as was occasionally observed in a preliminary study. No viable offspring developed from infected clutches, but 78% of the infected females produced healthy offspring after releasing the infected brood while molting. Neither those offsprings' development success nor their mothers' reproductive potential was affected by the brood parasite. However, infected Daphnia had a reduced life-span and suffered an increased susceptibility to another parasite, an unidentified bacterium. Additionally, we studied the prevalence of this brood parasite and the unidentified bacterium in a natural Daphnia assemblage in a pre-alpine lake, across changing demographic and environmental conditions. The brood parasite epidemic seemed to be host-density dependent. Our results show that the brood parasite's impact on the host population is enhanced when combined with the unidentified bacterium.

Environmental forcing, invasion and control of ecological and epidemiological systems

Destabilising a biological system through periodic or stochastic forcing can lead to significant changes in system behaviour. Forcing can bring about coexistence when previously there was exclusion; it can excite massive system response through resonance, it can offset the negative effect of apparent competition and it can change the conditions under which the system can be invaded. Our main focus is on the invasion properties of continuous time models under periodic forcing. We show that invasion is highly sensitive to the strength, period, phase, shape and configuration of the forcing components. This complexity can be of great advantage if some of the forcing components are anthropogenic in origin. They can be turned into instruments of control to achieve specific objectives in ecology and disease management, for example. Culling, vaccination and resource regulation are considered. A general analysis is presented, based on the leading Lyapunov exponent criterion for invasion. For unstructured invaders, a formula for this exponent can typically be written down from the model equations. Whether forcing hinders or encourages invasion depends on two factors: the covariances between invader parameters and resident populations and the shifts in average resident population levels brought about by the forcing. The invasion dynamics of a structured invader are much more complicated but an analytic solution can be obtained in quadratic approximation for moderate forcing strength. The general theory is illustrated by a range of models drawn from ecology and epidemiology. The relationship between periodic and stochastic forcing is also considered.

Seasonality of influenza in Brazil: a traveling wave from the Amazon to the subtropics

Influenza circulation and mortality impact in tropical areas have not been well characterized. The authors studied the seasonality of influenza throughout Brazil, a geographically diverse country, by modeling influenza-related mortality and laboratory surveillance data. Monthly time series of pneumonia and influenza mortality were obtained from 1979 to 2001 for each of the 27 Brazilian states. Detrended time series were analyzed by Fourier decomposition to describe the amplitude and timing of annual and semiannual epidemic cycles, and the resulting seasonal parameters were compared across latitudes, ranging from the equator (+5 degrees N) to the subtropics (-35 degrees S). Seasonality in mortality was most pronounced in southern states (winter epidemics, June-July), gradually attenuated toward central states (15 degrees S) (p < 0.001), and remained low near the equator. A seasonal southward traveling wave of influenza was identified across Brazil, originating from equatorial and low-population regions in March-April and moving toward temperate and highly populous regions over a 3-month period. Laboratory surveillance data from recent years provided independent confirmation that mortality peaks coincided with influenza virus activity. The direction of the traveling wave suggests that environmental forces (temperature, humidity) play a more important role than population factors (density, travel) in driving the timing of influenza epidemics across Brazil.

Effects of management and climate on elk brucellosis in the Greater Yellowstone Ecosystem

Every winter, government agencies feed approximately 6000 metric tons (6 x 10(6) kg) of hay to elk in the southern Greater Yellowstone Ecosystem (GYE) to limit transmission of Brucella abortus, the causative agent of brucellosis, from elk to cattle. Supplemental feeding, however, is likely to increase the transmission of brucellosis in elk, and may be affected by climatic factors, such as snowpack. We assessed these possibilities using snowpack and feeding data from 1952 to 2006 and disease testing data from 1993 to 2006. Brucellosis seroprevalence was strongly correlated with the timing of the feeding season. Longer feeding seasons were associated with higher seroprevalence, but elk population size and density had only minor effects. In other words, the duration of host aggregation and whether it coincided with peak transmission periods was more important than just the host population size. Accurate modeling of disease transmission depends upon incorporating information on how host contact rates fluctuate over time relative to peak transmission periods. We also found that supplemental feeding seasons lasted longer during years with deeper snowpack. Therefore, milder winters and/or management strategies that reduce the length of the feeding season may reduce the seroprevalence of brucellosis in the elk populations of the southern GYE.

Self-organization and productivity in semi-arid ecosystems: implications of seasonality in rainfall

Spatial self-organization including striking vegetation patterns observed in arid ecosystems has been studied in models with uniform rainfall. In this paper, we present a fully seasonal rainfall model that produces vegetation patterns found in nature by including the natural adaptation of plants to scarcity of water and the consequent seasonal variation in their growth and metabolic rate. We present results for the mean-field and spatially extended versions of the model. We find that the patterns depend on the duration of the wet season even with fixed total annual precipitation (PPT) showing how seasonality affects spatial self-organization. We observe that the productivity can vary for fixed PPT as a function of the duration thereby providing another source of observed variations. We compute the maximum vegetation cover as function of PPT and find that the behavior is consistent with observations. We comment on the implications for regime shifts due to increased interannual fluctuations caused by climatic changes. Our specific model calculations provide more general conclusions for ecosystems with competition for scarce resources due to seasonal variations in the resource, especially for self-organization and productivity.

The perpetuation and epidemic recurrence of communicable diseases in human populations

Recurrence of communicable diseases is a looming threat for human populations. Factors explaining the recurrences are partially known, involving demographics, biology, and complex relationships with the environment, but no comprehensive theory exists today. Here, we review some recent results obtained in modelling studies with a view to understanding better the mechanisms of perpetuation. Factors intrinsic to the interaction of pathogen and host have regained interest in this respect, especially with multiple pathogen and multiple population interactions. Extrinsic factors, including pure demography and environmental forcing are also strong predictors. With increasingly detailed data available, large-scale integrated models will help sorting out the multiple influences on recurrence. To cite this article: P.-Y. Boëlle, C. R. Biologies 330 (2007).

Environmental effects on parasitic disease transmission exemplified by schistosomiasis in western China

Environmental effects on the transmission of many parasitic diseases are well recognized, but the role of specific factors like climate and agricultural practices in modulating transmission is seldom characterized quantitatively. Based on studies of Schistosoma japonicum transmission in irrigated agricultural environments in western China, a mathematical model was used to quantify environmental impacts on transmission intensity. The model was calibrated by using field data from intervention studies in three villages and simulated to predict the effects of alternative control options. Both the results of these interventions and earlier epidemiological findings confirm the central role of environmental factors, particularly those relating to snail habitat and agricultural and sanitation practices. Moreover, the findings indicate the inadequacy of current niclosamide-praziquantel strategies alone to achieve sustainable interruption of transmission in some endemic areas. More generally, the analysis suggests a village-specific index of transmission potential and how this potential is modulated by time-varying factors, including climatological variables, seasonal water-contact patterns, and irrigation practices. These time-variable factors, a village's internal potential, and its connectedness to its neighbors provide a framework for evaluating the likelihood of sustained schistosomiasis transmission and suggest an approach to quantifying the role of environmental factors for other parasitic diseases.

Seasonal dynamics of recurrent epidemics

Seasonality is a driving force that has a major effect on the spatio-temporal dynamics of natural systems and their populations. This is especially true for the transmission of common infectious diseases (such as influenza, measles, chickenpox and pertussis), and is of great relevance for host-parasite relationships in general. Here we gain further insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR (susceptible, infectious or recovered) epidemic model. Our analysis differs from other modelling studies in that the focus is more on post-epidemic dynamics than the outbreak itself. Despite the mathematical intractability of the forced SIR model, we identify a new threshold effect and give clear analytical conditions for predicting the occurrence of either a future epidemic outbreak, or a 'skip'-a year in which an epidemic fails to initiate. The threshold is determined by the population's susceptibility measured after the last outbreak and the rate at which new susceptible individuals are recruited into the population. Moreover, the time of occurrence (that is, the phase) of an outbreak proves to be a useful parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-peaking diseases (that is, those having high phase) from spreading widely, thereby increasing population susceptibility, and controlling the triggering and intensity of future epidemics. These principles yield forecasting tools that should have relevance for the study of newly emerging and re-emerging diseases controlled by seasonal vectors.

Eating yourself sick: transmission of disease as a function of foraging ecology

Species interactions may profoundly influence disease outbreaks. However, disease ecology has only begun to integrate interactions between hosts and their food resources (foraging ecology) despite that hosts often encounter their parasites while feeding. A zooplankton-fungal system illustrated this central connection between foraging and transmission. Using experiments that varied food density for Daphnia hosts, density of fungal spores and body size of Daphnia, we produced mechanistic yet general models for disease transmission rate based on broadly applicable components of feeding biology. Best performing models could explain why prevalence of infection declined at high food density and rose sharply as host size increased (a pattern echoed in nature). In comparison, the classic mass-action model for transmission performed quite poorly. These foraging-based models should broadly apply to systems in which hosts encounter parasites while eating, and they will catalyse future integration of the roles of Daphnia as grazer and host.

Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population

The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R(0) of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p(0) (1+epsilon cos(omegat - phi)) with epsilon << 1. The first term is similar to the case of a constant vector population p but with p replaced by the average vector population p(0). The maximum correction due to the second term is (epsilon(2)/8)% and always tends to decrease R(0). The basic reproduction number R(0) is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R(0) are compared using as example a model for the 2005/2006 chikungunya epidemic in La Réunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality.

Seasonal infectious disease epidemiology

Seasonal change in the incidence of infectious diseases is a common phenomenon in both temperate and tropical climates. However, the mechanisms responsible for seasonal disease incidence, and the epidemiological consequences of seasonality, are poorly understood with rare exception. Standard epidemiological theory and concepts such as the basic reproductive number R0 no longer apply, and the implications for interventions that themselves may be periodic, such as pulse vaccination, have not been formally examined. This paper examines the causes and consequences of seasonality, and in so doing derives several new results concerning vaccination strategy and the interpretation of disease outbreak data. It begins with a brief review of published scientific studies in support of different causes of seasonality in infectious diseases of humans, identifying four principal mechanisms and their association with different routes of transmission. It then describes the consequences of seasonality for R0, disease outbreaks, endemic dynamics and persistence. Finally, a mathematical analysis of routine and pulse vaccination programmes for seasonal infections is presented. The synthesis of seasonal infectious disease epidemiology attempted by this paper highlights the need for further empirical and theoretical work.

Metabolic stress suppresses humoral immune function in long-day, but not short-day, Siberian hamsters (Phodopus sungorus)

Individuals of many species experience marked seasonal variation in environmental conditions and must adapt to potentially large fluctuations in energy availability and expenditure. Seasonal changes in immunity have likely evolved as an adaptive mechanism to cope with seasonal stressors. In addition, these changes may be constrained by seasonal fluctuations in energy availability. The goal of this study was to assess the role of energetic trade-offs associated with seasonal variation in immunity. In addition to body fat stores, metabolic fuels (e.g., glucose) may affect immune function in seasonally breeding rodents. In this study we experimentally reduced energy availability via injections of the metabolic inhibitor 2-deoxy-D-glucose (2-DG) in long- and short-day housed Siberian hamsters (Phodopus sungorus) and then examined antigen-specific antibody production. Metabolic stress decreased antibody response compared with control animals in long days. In contrast, no difference was observed between treatment groups in short days. These data suggest that reductions in energy availability suppress immunity and short days buffer organisms against glucoprivation-induced immunosuppression.

Urbanization and the ecology of wildlife diseases

Urbanization is intensifying worldwide, with two-thirds of the human population expected to reside in cities within 30 years. The role of cities in human infectious disease is well established, but less is known about how urban landscapes influence wildlife–pathogen interactions. Here, we draw on recent advances in wildlife epidemiology to consider how environmental changes linked with urbanization can alter the biology of hosts, pathogens and vectors. Although urbanization reduces the abundance of many wildlife parasites, transmission can, in some cases, increase among urban-adapted hosts, with effects on rarer wildlife or those living beyond city limits. Continued rapid urbanization, together with risks posed by multi-host pathogens for humans and vulnerable wildlife populations, emphasize the need for future research on wildlife diseases in urban landscapes.

How parasites affect interactions between competitors and predators

We present a synthesis of empirical and theoretical work investigating how parasites influence competitive and predatory interactions between other species. We examine the direct and indirect effects of parasitism and discuss examples of density and parasite-induced trait-mediated effects. Recent work reveals previously unrecognized complexity in parasite-mediated interactions. In addition to parasite-modified and apparent competition leading to species exclusion or enabling coexistence, parasites and predators interact in different ways to regulate or destablize the population dynamics of their joint prey. An emerging area is the impact of parasites on intraguild predation (IGP). Parasites can increase vulnerability of infected individuals to cannibalism or predation resulting in reversed species dominance in IGP hierarchies. We discuss the potential significance of parasites for community structure and biodiversity, in particular their role in promoting species exclusion or coexistence and the impact of emerging diseases. Ongoing invasions provide examples where parasites mediate native/invader interactions and play a key role in determining the outcome of invasions. We highlight the need for more quantitative data to assess the impact of parasites on communities, and the combination of theoretical and empirical studies to examine how the effects of parasitism scale up to community-level processes.