Age structured partial differential equations model for Culex mosquito abundance

Abstract

Mosquito borne diseases pose a significant health risk for humans. In North America, Culex mosquitoes are a major vector for several diseases including West Nile Virus and St. Louis Encephalitis. In many instances, models used to predict the spread of mosquito borne disease rely on a quantification of mosquito abundance. In our work, we present a novel age-structured partial differential equation model for simulating Culex mosquito abundance. The model is constructed using a system of two dimensional coupled advection reaction equations, in which the first dimension represents the age of the mosquitoes within a growth-stage population and the second dimension is time. We form six mosquito growth-stage populations by subdividing the mosquito life cycle into six stages: egg, larvae/pupae, and four adult gonotrophic cycles. Each growth-stage population is coupled through the boundary conditions on the age of the mosquito, which advances the population through its life cycle. The model also includes a population of diapausing adults represented using an ordinary differential equation. The solution curves for each equation provide the distribution of mosquitoes over time for each growth-stage population. This model provides information on the relative abundance of mosquitoes as well as the abundance of mosquitoes at specific ages. We simulate mosquito abundance for the Greater Ontario Area and compare the simulated adult abundance to mosquito trap count data. The model produces mosquito abundance patterns similar to those observed in trap count data.