Exploring the impact of temperature on the efficacy of replacing a wild Aedes aegypti population by a Wolbachia-carrying one

A non-autonomous time-delayed differential system, with time-varying delay, is proposed to reproduce the competitive dynamics of Wolbachia-infected and non-infected mosquito populations in several scenarios that differ by daily environmental temperature, the bacterial strain carried by the mosquito, and the guidelines for release of infected mosquitoes. Both mosquito entomological parameters and infection traits depend on temperature, which per se depends on time. Therefore, inspired by the literature on insect populations, functional forms are proposed to describe the rates of birth, development, and survival (or mortality) of Ae. aegypti as a function of temperature, as well as the rate of Wolbachia-infection loss. Numerical results showed that: (i) multiple releases were more efficient than a single one, (ii) when the mosquito population is high is the best time to implement the release of infected mosquitoes, (iii) strains that produce both high levels of cytoplasmic incompatibility and maternal inheritance boost the efficacy of the technique, and (iv) high temperature can jeopardize the efficacy of the technique.