Modeling Wolbachia infection in mosquito population via discrete dynamical models. (English) Zbl 1536.92156
Summary: 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 \(\mu^*\), such that infected mosquitoes can only persist if it is not exceeded by \(\mu^*\). When \(\mu\leq \mu^*\), we find the Wolbachia infection frequency threshold, denoted by \(p^*\), such that the infected mosquitoes can persist provided that the initial infection frequency \(x_0\geq p^*\). For the case when \(x_0<p^*\), we find the release rate threshold, denoted by \(\alpha^*\), for \(\alpha\in(0,\alpha^*)\), the Wolbachia infection frequency threshold is reduced, and for \(\alpha\geq\alpha^*\), the threshold infection frequency is further lowered to 0 which implies that Wolbachia persistence is always successful for any initial infection frequency above 0.
MSC:
| 92D30 | Epidemiology |
Keywords:
Wolbachia; cytoplasmic incompatibility; maternal transmission leakage rate; release threshold; unstable equilibriaReferences:
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