The Analysis Of A Several Of Types Of Epidemic Models

This paper mainly studys mathematical analysis of several types of epidemic models.In the case of an outbreak of an epidemic,psychological or medical resources are limited,the effect of information on a vaccination coverage play a major role in controlling the impact of the epidemic on society.This paper consists of four chapters:In Chapter 1,We outlined the critical point theory,preparations,historical background and the main works of this paper.In Chapter 2,We propose a time-delayed SIR epidemic model with Holling type IV treatment rate function,and discuss stability of the model at equilibrium points by considering Lyapunov function,and the Hopf bifurcation of the model at equilibrium points.Finally,we carry out numerical simulations using MATLAB.In Chapter 3,We propose a compartmental model(SVIM)which accounts for the effect of information on vaccination coverage,and compute the basic reproduction number and discuss the stability of the disease-free equilibrium.Second,we analyzed the optimal strategy.Finally,numerical simulations with MATLAB are performed to support the analytical findings.Therefore,the scale of infectious diseases can effectively be reduced.In Chapter 4,We propose a compartmental model(SIS)which time delay and aware.We establish a Lyapuunov Function for proving global stability of the disease free equilibrium,and then we found the existence of endemic equilibrium and the HOPF bifurcation.In the end,we use MATLAB for proving the correctness.