A Spatial Model to Describe the Dengue Propagation

Abstract

Dengue is a human disease transmitted by the mosquito Aedes aegypti. A dengue epidemic could start when infectious individuals (humans or mosquitoes) appear and could propagate in areas previously colonized by the mosquitoes. In this work, we propose a model to study the dengue propagation using a system of partial differential reaction-diffusion equations. The human and mosquito populations are considered, with their respective subclasses of infected and non infected populations. We assume that the diffusion occurs only in the winged form, and the human population is considered constant. The cross-infection is modeled by the mass action incidence law. A threshold value, as a function of the model’s parameters, is obtained, which determines the endemic level of the disease. Assuming that an area was previously colonized by the mosquitoes, the spread velocity of the disease propagation is determined as a function of the model’s parameters. The traveling waves solutions of the system of partial differential equations are considered to determine the spread velocity of the front wave.