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

Tailei Zhang

Applied Mathematics and Computation, 2015, vol. 271, issue C, 716-729

Abstract: 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 R0 is obtained for permanence versus extinction of disease. In order to illustrate our analytic analysis, some numerical simulations are also included in the end.

Keywords: Nonautonomous discrete epidemic model; Nonstandard finite difference scheme; Permanence; Extinction; Vaccination; Threshold conditions (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:271:y:2015:i:c:p:716-729

DOI: 10.1016/j.amc.2015.09.071

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