A Delay Differential Equations model for Wolbachia infection in Aedes aegypti populations

Abstract

Currently, Wolbachia is one of the most studied reproductive parasite of arthropod species and appears to be a promising candidate for biocontrol of some mosquito carried diseases, especially by Aedes aegypti. A mathematical model inspired by Nicholson-type delay equations is proposed to investigate the relation between temperature variation (implicit into maturation time) and population dynamics of both transinfected by a Wol- bachia strain and uninfected Aedes aegypti mosquitoes. We analyze the existence and local stability of equilibria with and without delay. [...]