The Analysis Of Dynamics Model Of Dengue Virus Transmission With Time Delay

In recent years,the research on the dynamic behavior of deterministic and stochastic infectious disea.se models with time delay has attracted extensive attention from scholars at home and abroad.A series of important research results were obtained.The dynamics models of deterministic vector-borne diseases with multiple time delays and stochastic vector-borne diseases are studied in this paper.The effects of time delay on disease prevention and control and random disturbance on the persistence and extinction of disease transmission are discussed.The main research contents can be summarized as follows:1.In the first part,The dynamical behavior of dengue virus transmission model with incubation delay is investigated.The local stability of the disease-free equilibrium and endemic equilibrium is obtained by using the linearization method and a new threshold condition on the disease free or endemic is established.Further,the global asymptotic stability of the positive equilibrium is proved by using Lyapunov functional method.Moreover,the sensitivity of threshold with respect to parameters is showed.Finally,the correctness of the theoretical results is illustrated by numerical simulations.2.In the second part,considering the incubation period of virus in mosquito body and the delay of media information,a dynamical model of dengue virus transmission with latency and media delay is proposed.By constructing appropriate Lyapunov func-tional and LaSalle invariance principle,the global asymptotic stability of disease-free equilibrium point is discussed.Furthermore,Hurwitz criterion and bifurcation theory are applied to analyze and discuss the sufficient conditions for the stability of endemic equilibrium and the existence of Hopf bifurcation under all different combinations of two kinds of delays.Finally,we execute several numerical simulations to illustrate the proposed mathematical model and our analytical findings.3.In the third part,a stochastic dengue virus transmission dynamics model with latency delay was established.By using the comparison principle of stochastic differential equation and Lyapunov analysis method,the existence and uniqueness of global positive solutions of the stochastic model are proved.Furthermore,sufficient conditions are obtained for the asymptotic behavior of the solution at the disease-free and endemic equilibrium points corresponding to the deterministic model.Finally,the theoretica.l results are verified by numerical simulation,and the effects of random perturbation and latency on dengue virus transmission are discussed.