Wolbachia infected and uninfected mosquito growth model using the Leslie multispecies matrix model

Abstract

Currently, there is a new strategy for stopping the spread of dengue, namely infecting wild mosquitoes with Wolbachia bacteria. Wolbachia is a bacteria that can lower the rate of infection in a mosquito's body, which lowers the risk of the virus being transmitted when it bites susceptible people. Our aim in this paper is to find the equilibrium points and perform local stability analysis for each equilibrium point of a growth model of uninfected and Wolbachia-infected Aedes aegypti mosquitoes. The growth model of the two types of mosquitoes was modeled using the Leslie multispecies matrix model. We assume that the first species is Wolbachia-uninfected mosquitoes and the second species is Wolbachia-infected mosquitoes. In this study, we obtained four equilibrium points. Then, we obtain asymptotically local stability conditions at the four equilibrium points. Based on these results, this study provides conditions that guarantee that efforts to use Wolbachia can suppress dengue disease.