Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination

• We formulate a discrete SIRVS epidemic model.
• The threshold conditions are expressed as inferior and superior limits of products.
• Dynamic behavior of the model is studied.
• A sharp threshold value is obtained under the case of periodic model.

In this paper, by applying a nonstandard finite difference scheme, we formulate a discretized SIRVS epidemic model which takes into account vaccination. Under quite weak assumptions, the threshold value conditions on permanence and extinction of disease are established. Some new threshold values in product forms R0* and R1* are obtained. We show that the disease is permanent if R0*>1, and if R1*<1, then the disease is extinct. When the model degenerates into a periodic model, a sharp threshold value R0R0 is obtained for permanence versus extinction of disease. In order to illustrate our analytic analysis, some numerical simulations are also included in the end.