Sufficient conditions are given which guarantee that the trivial solution x = 0 for a nonlinear integro–differential system is globally attracting. As an example, this result is applied to a SIRS epidemic model with subpopulations to show that, under certain conditions, the endemic equilibrium is globally asymptotically stable.

Some modified versions of susceptible-infected-recovered-susceptible (SIRS) model are defined on small-world networks. Latency, incubation and variable susceptibility are included, separately. Phase transitions in these models are studied. Then inhomogeneous models are introduced. In some cases, the application of the models to smallworld networks is shown to increase the epidemic region.

A modified version of susceptible-infected-recovered-susceptible (SIRS) model for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is defined on small-world networks, and a ring vaccination programme is included. This model can be a theoretical explanation for the nonlocal interactions in epidemic spreading. Ring vaccination is capable of eradicating FMD provided that the ...

In this paper, by extending well-known Lyapunov function techniques, we establish sufficient conditions for the global stability of an endemic equilibrium of a multi-group SIRS epidemic model with varying population sizes which has cross patch infection between different groups. Our proof no longer needs such a grouping technique by graph theory commonly used to analyze the multi-group SIR models.

This article deals with optimal control applied to vaccination and treatment strategies for an SIRS epidemic model with logistic growth and delay. The delay is incorporated into the model in order to modeled the latent period or incubation period. The existence for the optimal control pair is also proved. Pontryagin's maximum principle with delay is used to characterize these optimal controls. ...