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International Journal of Differential Equations
Volume 2017 (2017), Article ID 5796958, 14 pages
https://doi.org/10.1155/2017/5796958
Research Article

Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje 13615, 97119 Mérida, YUC, Mexico

Correspondence should be addressed to Eric Ávila-Vales

Received 25 July 2017; Revised 3 October 2017; Accepted 10 October 2017; Published 9 November 2017

Academic Editor: Khalid Hattaf

Copyright © 2017 Eric Ávila-Vales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form , and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.