Analysis Of Stability And Bifurcation For An SEIR Epidemic Model With Saturated Infection Rate And Treatment Function

This paper describes a traditional SEIR type epidemic model with saturated infection rate and treatment function.Here the treatment function adopts a continues and differ-entiable function which can describe the effect of delayed treatment when the number of infected individuals is getting larger and the medical condition is limited.It is shown that a backward bifurcation will appear when this delayed effect for treatment is strong,the basic reproduction number R0=1 is not a strict threshold for disease eradication,and a critical value at the turning point is deduced as a new threshold Rc.Some sufficient conditions for the disease-free equilibrium and the endemic equilibrium being globally asymptotically stable are obtained with the help of constructing the Lyapunov function and a geometric approach.Mathematical results in this paper suggests that giving the patients timely treatment is very important.Finally,some numerical simulations are done to prove the results of theoretical analysis.