Analysis Of An SIS Epidemic Model With Infective Vector Over Complex Network

The study on dynamics of infectious diseases provides theoretical basis and practical guidance for the control of diseases. It has important scientific research value and practical significance. Based on the background of malaria and yellow fever, this paper establishes an SIS epidemic model with the infective vector and multi-stage infection over complex network. It makes the model closer to reality.Chapter 1 introduces the necessity of infectious disease research and the research process of infectious disease with the infective vector, then we give the main work of this paper.In chapter 2, according to the transmission mechanism of malaria, we establish an SIS epidemic model with multiple infective vectors and multi-stage infection over complex networkwhereSk(t) = 1 - Ik(t),Ik(t)=?r=0TIk,r(t),?(t)=?k=1n kP(k)Ik(t).?(t)is the Probability of a link pointing to an infected individual, 0(t) =1/<k>?k=1nkP(k)Ik(t). Using relevant theoretical knowledge, the epidemic threshold A, of the model is derived. we also concluded that when R0< 1,the disease-free equilibrium is locally asymptotic stability; otherwise there exists an unique endemic equilibrium such that it is global asymptotic stability. Finally, the main results obtained in this chapter are verified by numerical simulation.In Chapter 3, considering the average incubation period of the disease in a vector, we establish an SIS epidemic model with the delay and infective vector where 0(t) =1/<k>?i=1n?(i)p(i)Ii(t).kAlso, we get the epidemic threshold. Finally, the correspond-ing numerical simulation is used to reflect the influence of the parameters in the process of disease transmission.In Chapter 4, we summarize the main conclusion of this paper and investigate some ideas for future research.