ModelingWolbachiainfection 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 μ∗, such that infected mosquitoes can only persist if it is not exceeded by μ∗. When μ≤μ∗, we find the Wolbachia infection frequency threshold, denoted by p∗, such that the infected mosquitoes can persist provided that the initial infection frequency x0≥p∗. For the case when x0<p∗, we find the release rate threshold, denoted by α∗, for α∈(0,α∗), the Wolbachia infection frequency threshold is reduced, and for α≥α∗, the threshold infection frequency is further lowered to 0 which implies that Wolbachia persistence is always successful for any initial infection frequency above 0.