The transmission of dengue virus with Aedes aegypti mosquito in a heterogeneous environment

This paper deals with dengue virus transmitted by the mosquito Aedes aegypti. A reaction-diffusion model is proposed incorporating both human and the A. aegypti population, where we divided mosquitoes into two sub-populations: the winged population and an aquatic form, with the winged mosquito population divided into the susceptible and infected classes. The threshold Q(0) depending on spatial heterogeneity is introduced for the mosquito population. Moreover, we introduce the basic reproduction number R-0 for the infected classes, as well as its analytical properties. Q(0) and R-0 are utilized to investigate the stability of the mosquito-established equilibriums. Our results show that the mosquitoes persist if Q(C) > 1, while the transmission of dengue virus depends on the condition whether R-0 < 1 or R-0 > 1.