  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.
