Mathematical analysis of a Wolbachia invasive model with imperfect maternal transmission and loss of Wolbachia infection

TL;DR

This paper presents a mathematical model analyzing Wolbachia's invasion dynamics in mosquito populations, accounting for imperfect maternal transmission and infection loss, crucial for designing effective vector control strategies.

Contribution

It introduces a novel transmission model incorporating imperfect maternal transmission and infection loss, deriving invasion thresholds and stability conditions.

Findings

Imperfect maternal transmission can prevent Wolbachia establishment despite cytoplasmic incompatibility.

Optimal release strategies depend on transmission fidelity and infection loss rates.

The model guides decision-making for mosquito population replacement or coexistence.

Abstract

Arboviral infections, especially dengue, continue to cause significant health burden in their endemic regions. One of the strategies to tackle these infections is to replace the main vector agent, Ae. aegypti, with the ones incapable of transmitting the virus. Wolbachia, an intracellular bacterium, has shown promise in achieving this goal. However, key factors such as imperfect maternal transmission, loss of Wolbachia infection, reduced reproductive capacity and shortened life-span affect the dynamics of Wolbachia in different forms in the Ae. aegypti population. In this study, we developed a Wolbachia transmission dynamic model adjusting for imperfect maternal transmission and loss of Wolbachia infection. The invasive reproductive number that determines the likelihood of replacement of the Wolbachia-uninfected (WU) population is derived and with it, we established the local and global stability of the equilibrium points. This analysis clearly shows that cytoplasmic incompatibility (CI) does not guarantee establishment of the Wolbachia-infected (WI) mosquitoes as imperfect maternal transmission and loss of Wolbachia infection could outweigh the gains from CI. Optimal release programs depending on the level of imperfect maternal transmission and loss of Wolbachia infection are shown. Hence, it is left to decision makers to either aim for replacement or co-existence of both populations.