Mathematical Analysis of a Periodic Delay Differential System for Mosquito Population Suppression Using Wolbachia-Infected Males Releases

This paper presents a mathematical analysis of a nonautonomous delay differential system. This system models mosquito population dynamics under the influence of seasonal environmental fluctuations and a biological control strategy based on the continuous release of Wolbachia-infected males. The model extends previous frameworks by incorporating a maturation delay for aquatic stages and time-periodic coefficients for all demographic parameters, thereby capturing two essential biological features: the developmental lag between aquatic and adult stages and the seasonal variability in fecundity, carrying capacity, and mortality rates. We establish the well-posedness of the system by proving existence, uniqueness, positivity, and boundedness of solutions. Using the theory of semiflows and comparison principles for functional differential equations, we derive the basic offspring number Rv in a periodic environment with delay via the next-generation operator approach. A sharp threshold dynamics is demonstrated: When Rv 1, the system exhibits uniform persistence and admits at least one positive periodic solution. Extensive numerical simulations illustrate the theoretical findings and investigate the sensitivity of population dynamics to key parameters, including the maturation delay and the amplitude of seasonal variations in oviposition rate and carrying capacity.