Two-sex mosquito model for the persistence of Wolbachia

TL;DR

This paper presents a mathematical model analyzing Wolbachia transmission in mosquitoes, revealing conditions for establishing infection despite a basic reproduction number below one, emphasizing the importance of reducing wild populations beforehand.

Contribution

It introduces a two-sex mosquito model incorporating Wolbachia effects and demonstrates the threshold conditions for infection establishment through bifurcation analysis.

Findings

Endemic Wolbachia infection can be established with sufficient release numbers.

A backward bifurcation creates multiple stable states affecting infection persistence.

Reducing wild mosquito populations enhances infection establishment success.

Abstract

Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit dengue virus. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to establish an endemic infection in a wild mosquito population. We developed and analyzed an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachia-infected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Our transmission model for the adult and aquatic-stage mosquitoes takes into account Wolbachia-induced fitness change and cytoplasmic incompatibility. We showed that, for a wide range of realistic parameter values, the basic reproduction number is less than one. Hence, the epidemic will die out if only a few Wolbachia-infected mosquitoes are introduced into the wild population. Even though the basic reproduction number is less than one, an endemic Wolbachia infection can be established if a sufficient number of infected mosquitoes are released. This threshold effect is created by a backward bifurcation with three coexisting equilibria: a stable zero-infection equilibrium, an intermediate-infection unstable endemic equilibrium, and a high-infection stable endemic equilibrium. We analyzed the impact of reducing the wild mosquito population before introducing the infected mosquitoes and observed that the most effective approach to establish the infection in the wild is based on reducing mosquitoes in both the adult and aquatic stages.