Vaccination Strategies Of Epidemic Model With Latent Period

With the development of society, food, clothing, shelter and transportation become abundant in recent years. But then various sudden infectious diseases are following, which now threaten the quality of human life. For some infectious disease, an individual goes through a period time from being transmitted to the disease, which may be a few days, or may be decades. We call it latent period. In this paper, the epidemic models with latent period are studied.First, we mainly introduce the research significance, progress and development direction of studying infectious disease model, and introduce the related basic knowledge for this paper, and then give the problems studied of this paper.Second, we establish an SEIQR model with constant input and nonlinear incidence, and get the threshold value of the disease popularity0 R. By using Lasalle invariant principle, we prove that the disease-free equilibrium is global asymptotical stability when 10R?, and by using the second additive compound matrix, we prove that the endemic equilibrium is global asymptotical stability when 11R?.Next, we establish a delayed SEIR epidemic model with vertical transmission and impulsive vaccination. Using the Floquet theorem and comparison theorem of impulsive differential equation, we discuss the global attractive of the disease-free periodic solution, and obtain the sufficient conditions of the permanence for the system with delay.Finally, we establish a double-delayed SEIRS model with saturated infection rate and impulsive vaccination. The double-delayed is caused by two parts of reasons, partly because the disease has certain latent period and on the other hand it takes a while from infected to remover. Using comparison theorem of impulsive differential equation, we prove the global attractivity of the disease-free periodic solution, and using V function we prove the permanence for the system. Numerical simulations are carried out to illustrate the main results.