A Seasonal Model for West Nile Virus

West Nile virus (WNV) is maintained in transmission cycles involving bird reservoir hosts and mosquito vectors. While several aspects of the infection cycle have been explored through mathematical models, relatively little attention has been paid to the theoretical effect of seasonal changes in host and vector densities. Here we consider a model for the transmission dynamics of WNV in a temperate climate, where mosquitoes are not active during winters, so that infection dynamics can be described through a sequence of discrete growing seasons. Within-season host and vector demography is described through phenomenological functions of time describing fertility, mortality and migration. Over-wintering of infection is assumed to occur through diapausing mosquito females, with or without vertical transmission. We introduce a parameter S-0 that, similarly to R-0 but easier to compute, yields a threshold condition for infection persistence in this semi-discrete setting. Then we study the possible dynamical behavior of the model, by exploring parameter values through a Latin Hypercube Sampling and accepting only those values yielding solutions respecting a few conditions obtained from the qualitative patterns observed in yearly patterns of mosquito abundance and virus prevalence. For some parameters the posterior distribution is rather narrow, implying that simple qualitative agreement with data can yield information on parameter difficult to estimate directly. For other parameters, the posterior distribution is instead similar to the prior. Simulations of multi-year dynamics after a first introduction of the virus always asymptotically result, if S-0 > 1, in a pattern of yearly identical infections; however, their amplitude may be very different, even for the same value of S-0, in correspondence to the uncertainties about several parameters.