Abstract
Many infectious diseases exhibit seasonal dynamics driven by periodic fluctuations of the environment. Predicting the risk of pathogen emergence at different points in time is key for the development of effective public health strategies. Here we study the impact of seasonality on the probability of emergence of directly transmitted pathogens under different epidemiological scenarios. We show that when the period of the fluctuation is large relative to the duration of the infection, the probability of emergence varies dramatically with the time at which the pathogen is introduced in the host population. In particular, we identify a new effect of seasonality (the winter is coming effect) where the probability of emergence is vanishingly small even though pathogen transmission is high. We use this theoretical framework to compare the impact of different preventive control strategies on the average probability of emergence. We show that, when pathogen eradication is not attainable, the optimal strategy is to act intensively in a narrow time interval. Interestingly, the optimal control strategy is not always the strategy minimizing R0, the basic reproduction ratio of the pathogen. This theoretical framework is extended to study the probability of emergence of vector borne diseases in seasonal environments and we show how it can be used to improve risk maps of Zika virus emergence.
Highlights
The development of effective control strategies against the emergence or re-emergence of pathogens requires a better understanding of the early steps leading to an outbreak [1, 2, 3, 4].Classical models in mathematical epidemiology predict that whether or not an epidemic emerges depends on R0 1⁄4l m the basic reproduction ratio of the pathogen, where λ is the birth rate of the infection and μ is the death rate of the infection
Seasonality drives fluctuations in the probability of pathogen emergence, with dramatic consequences for public health and agriculture. We show that this probability of pathogen emergence can be vanishingly small before the low transmission season
We derive the conditions for the existence of this winter is coming effect and identify optimal control strategies that minimize the risk of pathogen emergence
Summary
The development of effective control strategies against the emergence or re-emergence of pathogens requires a better understanding of the early steps leading to an outbreak [1, 2, 3, 4].Classical models in mathematical epidemiology predict that whether or not an epidemic emerges depends on R0 1⁄4l m the basic reproduction ratio of the pathogen, where λ is the birth rate of the infection (a function of the transmission rate and the density of susceptible hosts) and μ is the death rate of the infection (a function of the recovery and mortality rates). In the classical deterministic description of disease transmission, the pathogen will spread if R0 > 1 and will go extinct otherwise (Fig 1). This deterministic description of pathogen invasion relies on the underlying assumption that the initial number of introduced pathogens is large. The early stages of an invasion are, typically characterized by a small number, n, of infected hosts. These populations of pathogens are very sensitive to demographic stochasticity and may be driven to extinction even when R0 > 1.
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