Stability Analysis For Infectious Disease Models With Nonlinear Incidence Rate And Delay

In recent years, many scholars investigated the infectious disease model by using the theory of delay differential equations, and some important conclusions are obtained.In this paper, we discussed the stability of SIR, SIRS epidemic models.The main contents are as follows:In the first part, we formulate a class of SIR epidemic model with delay and transmission rate of βSⁿ.Then, by using the basic reproductive number R₀,Hurwitz judgment and La Salle invariable principle, we give the sufficient conditions on locally asymptotic stability and global asymptotic stability of the model.In the second part, we establish a class of SIRS epidemic model with delay and transmission rate of. Then, we obtain the sufficient conditions on locally asymptotic stability and global asymptotic stability of the model with the help of the basic reproductive number R₁,Hurwitz judgment, iterative technique and the comparison principle.In the third part, on the basis of the second part, we set up a class of SIRS model with nonlinear infection rate and double delay. We obtain the sufficient conditions on locally asymptotic stability and global asymptotic stability of the model.