Analysis of dengue hemorrhagic fever model with logistic growth rate in aquatic stage

Dengue Hemorrhagic Fever (DHF) is carried by the female Aedes aegypti mosquito. This mosquito nests in clear water reservoirs. The mosquito life cycle originates from the water phase, namely egg, larva and pupa. In this paper, we construct and analysis the model of DHF transmission with logistic growth rate in water phase. In this work, the namely of Rn is a sign of the presence of mosquitoes. The results of the model analysis obtained three equilibria, namely the disease-free equilibrium (DFE) without mosquito presence, the DFE with mosquito presence (exist if Rn > 1) and the endemic equilibrium (exist if Rn > 1). The DFE with mosquito presence is locally and globally asymptotically stable if the reproduction number R0 < 1, and the endemic equilibrium is globally asymptotically stable if R0 > 1.