Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate

A Delayed Sir Epidemic Model with General Incidence Rate

A delayed SIR epidemic model with a generalized incidence rate is studied. The time delay represents the incubation period. The threshold parameter, R0(τ) is obtained which determines whether the disease is extinct or not. Throughout the paper, we mainly use the technique of Lyapunov functional to establish the global stability of both the disease-free and endemic equilibrium.

Permanence and extinction for a nonautonomous SEIRS epidemic model

In this paper, we study the long-time behavior of a nonautonomous SEIRS epidemic model. We obtain new su cient conditions for the permanence (uniform persistence) and extinction of infectious population of the model. By numerical examples we show that there are cases such that our results improve the previous results obtained in [T. Zhang and Z. Teng, On a nonautonomous SEIRS model in epidemiol...

Existence of a Nonautonomous SIR Epidemic Model with Age Structure

Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis ‎Incidence Rate and a Constant Infectious Period

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...

Permanence and extinction for a nonautonomous SVIR epidemic model with distributed time delay∗

In this paper we have considered a nonautonomous SV IR epidemic model with varying total population size and distributed time delay to become infectious. Instead of assuming that vaccinees gain immunity immediately, we have assumed that they are different from susceptible and recovered persons and it takes some time for them to gain immunity and then enter into the recovered class. Here, we hav...