Seasonality and the persistence of vector-borne pathogens.

Many vector-borne diseases are affected by the seasonality of the environment. Yet, seasonality can act on distinct steps of the life cycle of the pathogen and it is often difficult to predict the influence of the periodic fluctuations of the environment on the basic reproduction ratio of vector-borne pathogens. Here, we analyse a general vector-borne disease model and we account for periodic fluctuations of different components of the pathogen's life cycle. We develop a perturbation analysis framework to obtain useful approximations to evaluate the overall consequences of seasonality on the of the pathogen. This analysis reveals when seasonality is expected to increase or to decrease pathogen persistence. We show that seasonality in vector density or in the biting rate of the vector can have opposite effects on persistence and we provide a useful biological explanation for this result based on the covariance between key compartments of the epidemiological model. This framework could be readily extended to explore the influence of seasonality on other components of the life cycle of vector-borne pathogens.