Modeling Wolbachia infection in mosquito population via discrete dynamical models

We formulate discrete dynamical models to study Wolbachia infection persistence by releasing Wolbachia-infected mosquitoes, which display rich dynamics including bistable, semi-stable and globally asymptotically stable equilibria. Our analysis shows a maximal maternal leakage rate threshold, denoted by , such that infected mosquitoes can only persist if it is not exceeded by . When , we find the Wolbachia infection frequency threshold, denoted by , such that the infected mosquitoes can persist provided that the initial infection frequency . For the case when , we find the release rate threshold, denoted by , for , the Wolbachia infection frequency threshold is reduced, and for , the threshold infection frequency is further lowered to 0 which implies that Wolbachia persistence is always successful for any initial infection frequency above 0.