Pejman Rohani

Appropriate Models for the Management of Infectious Diseases

Background Mathematical models have become invaluable management tools for epidemiologists, both shedding light on the mechanisms underlying observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. Here, we explain how substantial biases are introduced by two important, yet largely ignored, assumptions at the core of the vast majority of such models. Methods and Findings First, we use analytical methods to show that (i) ignoring the latent period or (ii) making the common assumption of exponentially distributed latent and infectious periods (when including the latent period) always results in underestimating the basic reproductive ratio of an infection from outbreak data. We then proceed to illustrate these points by fitting epidemic models to data from an influenza outbreak. Finally, we document how such unrealistic a priori assumptions concerning model structure give rise to systematically overoptimistic predictions on the outcome of potential management options. Conclusion This work aims to highlight that, when developing models for public health use, we need to pay careful attention to the intrinsic assumptions embedded within classical frameworks.

Seasonnally forced disease dynamics explored as switching between attractors

Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This ‘binary’ nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella.

Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion

Understanding the transmission dynamics and persistence of avian influenza viruses (AIVs) in the wild is an important scientific and public health challenge because this system represents both a reservoir for recombination and a source of novel, potentially human-pathogenic strains. The current paradigm locates all important transmission events on the nearly direct fecal/oral bird-to-bird pathway. In this article, on the basis of overlooked evidence, we propose that an environmental virus reservoir gives rise to indirect transmission. This transmission mode could play an important epidemiological role. Using a stochastic model, we demonstrate how neglecting environmentally generated transmission chains could underestimate the explosiveness and duration of AIV epidemics. We show the important pathogen invasion implications of this phenomenon: the nonnegligible probability of outbreak even when direct transmission is absent, the long-term infectivity of locations of prior outbreaks, and the role of environmental heterogeneity in risk.

Persistence, chaos and synchrony in ecology and epidemiology

The decline of species in natural habitats concerns ecologists, who view extinction as a danger and conservation of biological diversity as a goal. In contrast, the proliferation of ‘undesirable’ species is the principal concern of epidemiologists, who view persistence as a problem and eradication as an achievement. While ecologists and epidemiologists have essentially opposite goals, the mathematical structure of the population dynamics that they study is very similar. We briefly review the similarities and differences between these two fields, emphasizing recent work in both areas on the effects of spatial synchrony and dynamical chaos. We hope to stimulate further cross–fertilization of ideas between the disciplines.

The interplay between determinism and stochasticity in childhood diseases

An important issue in the history of ecology has been the study of the relative importance of deterministic forces and processes noise in shaping the dynamics of ecological populations. We address this question by exploring the temporal dynamics of two childhood infections, measles and whooping cough, in England and Wales. We demonstrate that epidemics of whooping cough are strongly influenced by stochasticity; fully deterministic approaches cannot achieve even a qualitative fit to the observed data. In contrast, measles dynamics are extremely well explained by a deterministic model. These differences are shown to be caused by their contrasting responses to dynamical noise due to different infectious periods.

The Role of Environmental Transmission in Recurrent Avian Influenza Epidemics

Avian influenza virus (AIV) persists in North American wild waterfowl, exhibiting major outbreaks every 2–4 years. Attempts to explain the patterns of periodicity and persistence using simple direct transmission models are unsuccessful. Motivated by empirical evidence, we examine the contribution of an overlooked AIV transmission mode: environmental transmission. It is known that infectious birds shed large concentrations of virions in the environment, where virions may persist for a long time. We thus propose that, in addition to direct fecal/oral transmission, birds may become infected by ingesting virions that have long persisted in the environment. We design a new host–pathogen model that combines within-season transmission dynamics, between-season migration and reproduction, and environmental variation. Analysis of the model yields three major results. First, environmental transmission provides a persistence mechanism within small communities where epidemics cannot be sustained by direct transmission only (i.e., communities smaller than the critical community size). Second, environmental transmission offers a parsimonious explanation of the 2–4 year periodicity of avian influenza epidemics. Third, very low levels of environmental transmission (i.e., few cases per year) are sufficient for avian influenza to persist in populations where it would otherwise vanish.

Contact Network Structure Explains the Changing Epidemiology of Pertussis

Coughing Back Resurgence of whooping cough (or pertussis) is problematic because of the risk of infant fatality, but it has been occurring despite the availability of a vaccine. Data from Sweden, where national vaccination for whooping cough was discontinued for 17 years, before resumption in 1996, was used by Rohani et al. (p. 982) to build a model that showed that age-specific social contacts were an important influence on the spread of infection. The model helped to explain why resumption of vaccination was so successful in curbing infant whooping cough but had no effect on pertussis in adolescents. The model thus demonstrated how potentially important it is to take account of age-stratification in a population when considering public health policy. Age-specific social networks can influence transmission of infection and should be considered in health policy planning. The epidemiology of whooping cough (pertussis) remains enigmatic. A leading cause of infant mortality globally, its resurgence in several developed nations—despite the availability and use of vaccines for many decades—has caused alarm. We combined data from a singular natural experiment and a detailed contact network study to show that age-specific contact patterns alone can explain shifts in prevalence and age-stratified incidence in the vaccine era. The practical implications of our results are notable: Ignoring age-structured contacts is likely to result in misinterpretation of epidemiological data and potentially costly policy missteps.

Interactions between serotypes of dengue highlight epidemiological impact of cross-immunity

Dengue, a mosquito-borne virus of humans, infects over 50 million people annually. Infection with any of the four dengue serotypes induces protective immunity to that serotype, but does not confer long-term protection against infection by other serotypes. The immunological interactions between serotypes are of central importance in understanding epidemiological dynamics and anticipating the impact of dengue vaccines. We analysed a 38-year time series with 12 197 serotyped dengue infections from a hospital in Bangkok, Thailand. Using novel mechanistic models to represent different hypothesized immune interactions between serotypes, we found strong evidence that infection with dengue provides substantial short-term cross-protection against other serotypes (approx. 1–3 years). This is the first quantitative evidence that short-term cross-protection exists since human experimental infection studies performed in the 1950s. These findings will impact strategies for designing dengue vaccine studies, future multi-strain modelling efforts, and our understanding of evolutionary pressures in multi-strain disease systems.

Ecological interference between fatal diseases.

An important issue in population biology is the dynamic interaction between pathogens. Interest has focused mainly on the indirect interaction of pathogen strains, mediated by cross immunity. However, a mechanism has recently been proposed for ‘ecological interference’ between pathogens through the removal of individuals from the susceptible pool after an acute infection. To explore this possibility, we have analysed and modelled historical measles and whooping cough records. Here we show that ecological interference is particularly strong when fatal infections permanently remove susceptibles. Disease interference has substantial dynamical consequences, making multi-annual outbreaks of different infections characteristically out of phase. So, when disease prevalence is high and is associated with significant mortality, it might be impossible to understand epidemic patterns by studying pathogens in isolation. This new ecological null model has important consequences for understanding the multi-strain dynamics of pathogens such as dengue and echoviruses.

Spatial self-organisation in ecology: pretty patterns or robust reality?

Many seemingly plausible mathematical models of small-scale ecological interactions predict the self-organisation of dynamic, coherent and large scale spatial patterns (e.g. spirals). If true, such patterns would have important ecological and evolutionary consequences. For the most part, however, empirical studies have not corroborated their existence, suggesting erroneous dynamics in the models, shortcomings in empirical methodology, or both. Arguments for categorically dismissing self-organized patterns have been based on their assumed sensitivity to symmetry-breaking stochastic noise. However, many plausible mechanisms for generating patterns are robust to noise, and consequently broken symmetry is insufficient grounds for dismissing these self-organized patterns.