Modeling Wolbachia infection in mosquito population via discrete dynamical models

ABSTRACT

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 ${\mu }^{\ast }$, such that infected mosquitoes can only persist if it is not exceeded by ${\mu }^{\ast }$. When $\mu \le {\mu }^{\ast }$, we find the Wolbachia infection frequency threshold, denoted by $p^{\ast }$, such that the infected mosquitoes can persist provided that the initial infection frequency $x_0\ge p^{\ast }$. For the case when $x_0<p^{\ast }$, we find the release rate threshold, denoted by ${\alpha }^{\ast }$, for $\alpha \in (0,{\alpha }^{\ast })$, the Wolbachia infection frequency threshold is reduced, and for $\alpha \ge {\alpha }^{\ast }$, the threshold infection frequency is further lowered to 0 which implies that Wolbachia persistence is always successful for any initial infection frequency above 0.

KEYWORDS:

• Wolbachia
• cytoplasmic incompatibility
• maternal transmission leakage rate
• the release threshold
• unstable equilibria

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 92B05
• 92D30
• 37N25

Acknowledgements

We thank the three reviewers' valuable and precious suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (11971127, 11826302, 11631005, 11871174).