Estudo do comportamento antropofílico de mosquitos selvagens e transgênicos baseado em um modelo de reação-difusão-quimiotaxia

Abstract

Mosquito-borne diseases such as dengue, malaria, chikungunya, Zika-virus and yellow fever, have been relevant subject of studies in the academic- scientific environment. The alarming numbers reported yearly in the world place many of these diseases in prominence. Genetic manipulation techniques, together with prevention methods, vaccines and drug treatment provide a set of possibilities that, when used correctly, can considerably reduce the incidence of many diseases. The assessment of disease prevention and control measures must first be done through simulations of mathematical and computational models and just later practical application in order to guarantee safety, economy and viability. In this work, we propose a model described by a system of differential equations of the reaction-diffusion-chemotaxis type that describes the spread and interaction between wild and transgenic mosquitoes, where the transgenic population has a reduced CO2 detection capacity, which makes it difficult to blood orientation and therefore reduces the bitting rate on humans. The model was solved numerically using the sequential operator splitting technique, with the reactive part of the system solved by the fourth-order Runge-kutta and the diffusive-chemotactic part by the Crank-Nicolson method. The numerical simulations obtained attest to the consistency of the model with the assumptions adopted.