Existence and stability of periodic solutions for a mosquito suppression model with incomplete cytoplasmic incompatibility

Abstract

Cytoplasmic incompatibility (CI) caused by endosymbiotic bacteria Wolbachia has been an effective way to suppress and even eradicate wild vector mosquitoes. By assuming that CI is driven by impulsive and periodic releases of Wolbachia-infected males, we develop a time-switching ordinary differential equation model to characterize the impact of the release amount, the release period and the incomplete CI on the suppression efficiency. Sufficient conditions to guarantee the existence and uniqueness, or the existence of exactly two periodic solutions are obtained, together with their stability analyses.

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