Mathematical analysis of a <i>Wolbachia</i> invasive model with imperfect maternal transmission and loss of <i>Wolbachia</i> infection.

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, <i>Ae. aegypti</i>, with the ones incapable of transmitting the virus. <i>Wolbachia</i>, an intracellular bacterium, has shown promise in achieving this goal. However, key factors such as imperfect maternal transmission, loss of <i>Wolbachia</i> infection, reduced reproductive capacity and shortened life-span affect the dynamics of <i>Wolbachia</i> in different forms in the <i>Ae. aegypti</i> population. In this study, we developed a <i>Wolbachia</i> transmission dynamic model adjusting for imperfect maternal transmission and loss of <i>Wolbachia</i> infection. The invasive reproductive number that determines the likelihood of replacement of the <i>Wolbachia</i>-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 <i>Wolbachia</i>-infected (WI) mosquitoes as imperfect maternal transmission and loss of <i>Wolbachia</i> infection could outweigh the gains from CI. Optimal release programs depending on the level of imperfect maternal transmission and loss of <i>Wolbachia</i> infection are shown. Hence, it is left to decision makers to either aim for replacement or co-existence of both populations.