Modeling And Dynamic Analysis Of Two Classes Of Dengue

Dengue fever is an acute infectious disease caused by dengue virus and mainly transmitted by Aedes mosquito.The characteristics of this disease have high morbidity,rapid transmission,and high mortality in severely ill patients and so on.Therefore,the research on dengue infectious diseases has become a hot topic at present.In this paper,we propose two types of dengue epidemic models: a dengue model with vertical propagation and a dengue model with two types of hosts.Based on the stability theory of ordinary differential equations and singular perturbation theory,the eigenvalue analysis method,Lyapunov function method,and scale separation are used to discuss the stability of the equilibria,and consistent persistence for the proposed models.The effects of vertical propagation of mosquitoes and multi-hosts on the dynamic behavior of the model are considered,and some meaningful results are obtained.This paper is organized as follows :1.The dengue model with vertical propagation is discussed.The global stability of the disease-free equilibrium and endemic equilibrium is proved by using Lyapunov function method.Taking into account the differences between human and mosquito time scales,the original system is separated into fast and slow subsystems.Then the global stability of the disease-free equilibrium and endemic equilibrium of the slow system are discussed.2.A vector-host dengue model with two-hosts is discussed.Using the stability theory of differential equations,the stability of disease-free equilibrium,the existence and endurance of endemic equilibrium are studied,and numerical simulations are used to verify results of theoretical analysis.