Modelagem matemática do uso da bactéria Wolbachia como meio de controle da população de mosquitos Aedes aegypti

Abstract

Due to the difficulty in combating the highly reproductive population of Aedes aegypti, dengue has become a worldwide public health problem. Despite the efforts of the government, which employs control methods, especially the chemical and mechanical ones, the initiatives are still insufficient. In an attempt to reduce dengue cases, an alternative method is to use biological control of the transmitting vector through the Wolbachia bacterium. In general, this technique interacts the population of wild mosquitoes with mosquitoes contaminated with the bacteria, aiming to shorten the longevity of the insect and alter its fecundity, given that under certain conditions there is a possibility that the entire population of wild mosquitoes will contract the bacteria. Therefore, the general objective of the present work will be to analyze the dynamics and propagation of Wolbachia in natural populations of the Aedes aegypti mosquito. Therefore, mathematical modeling will be used to describe the interaction between infected and uninfected populations. The proposed model results in a reaction-diffusion type system that will be solved using the sequential operator splitting technique, which combines the Runge-kutta method and the finite difference method for the reaction and diffusion operators, respectively.