On the analysis of parasite effect for Aedes aegypti and Aedes albopictus population

It has been reported in some countries that the population of Aedes aegypti has been significantly reduced by the invasion of Aedes albopictus. There has been a hypothesis explaining this phenomenon of which investigated the influence of parasites pathogenesis to the competition between these two mosquito species in the fields. Ascogregarina taiwanensis and Ascogregarina culicis are known as parasites that infect Aedes albopictus and Aedes aegypti, respectively. Several studies have concluded that Ascogregarina taiwanensis caused high fatality for Aedes aegypti larvae, but Ascogregarina culicis was not pathogenic to Aedes albopictus larvae. Therefore, Ascogregarina taiwanensis may contribute to reduce the number of populations Aedes aegypti in the fields. Inspired by these facts, a mathematical model depicting interaction between parasites and mosquitoes is constructed in this paper. In this model are included six dynamic mosquito compartments, i.e. egg, larvae, infected larvae, adult, infected adult and one dynamic compartment for parasite. Derivation of the existence criteria and the stability analysis of parasite-free equilibrium as well as the basic offspring for the model are presented. Numerical simulations for sensitivity analysis indicating the invasive species for variation parameters are shown.