Wolbachia infection enhancing and decaying domains in mosquito population based on discrete models

Abstract

In this article, we formulate and study a discrete equation model depicting the pattern of Wolbachia infection in a mosquito population. A domain in $\mathcal {R}_+^2 $ is called a Wolbachia infection enhancing (or decaying) domain if in which the Wolbachia infection frequency of the next generation is always bigger (or smaller) than that of the current generation. We first give a complete analysis of the equivalent Wolbachia infection frequency curves. And then we clearly characterize the Wolbachia infection enhancing domain and decaying domain for all of the parameters, respectively. Finally, some numerical examples are also provided to illustrate our theoretical results.

Keywords

• wolbachia
• cytoplasmic incompatibility
• maternal transmission
• leakage rate
• wolbachia infection
• enhancing domain
• decaying domain