Dynamical Analysis Of A Vector-borne Disease Model Incorporating Stochastic Perturbations

Infectious disease dynamics is mainly devoted to theoretically studying the spread and development of infectious diseases,looking for the main factors leading to the epidemic of the disease.In recent years,more and more scholars and experts have drawn great attentions on the establishment and academic research of mathematical models of infectious diseases.In this dissertation,we involve a deterministic SEIRS-SI vector-borne disease model and then extend this model by introducing random perturbations into the model to the stochastic models.By mainly applying the It? lemma and other methods,we do the analysis of the dynamical system and then study the stability of the infectious disease models.The dissertation consists of five parts.In Chapter 1,we introduce the background and some recent researches of the paper,and the main work in this dissertation.In Chapter 2,some definitions and preliminary theorems which would be used in this dissertation are introduced specifically.In Chapter 3,we propose a 6-dimensional deterministic ODE model which keeps track of both host and vector populations and uses standard incidence terms to model the transmission of the disease in order to study the vector-borne disease transmission.First,the stability of the equilibrium is characterized in terms of an explicitly determined basic reproduction number obtained via the next generation method.Then,to examine the effects of a randomly fluctuating environment,we introduce multiple perturbations of white noise type and discuss the asymptotic behavior of the solutions of the corresponding stochastic model around the steady states of the initial deterministic model of the disease-free equilibrium and the endemic equilibrium.Finally,we give the numerical simulation to illustrate our mathematical results.In Chapter 4,we propose and investigate a stochastic model for a vector-borne disease by introducing stochastic perturbations in the term of the contact rate.Existence,unique and positive global solution of our stochastic model are investigated.Subsequently,the boundedness of solutions of the corresponding system is established.Then we investigate the moment exponential stability of the disease-free steady by constructing the Lyapunov function and applying the Young's inequality.Finally,some simulations are given to illustrate our mathematical findings.In the last chapter,we make a summary of the dissertation.