Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume -, Issue -, Pages -Publisher
SPRINGEROPEN
DOI: 10.1186/s13662-015-0429-3
Keywords
SEIRS epidemic model; generalized non-linear incidence rate; basic reproduction number; global stability; numerical simulations
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Funding
- Ministry of Education Malaysia (MOEM)
- Research Management Centre UTM [06H67, 4F255]
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In this paper, we present the global dynamics of an SEIRS epidemic model for an infectious disease not containing the permanent acquired immunity with non-linear generalized incidence rate and preventive vaccination. The model exhibits two equilibria: the disease-free and endemic equilibrium. The disease-free equilibrium is stable locally as well as globally when the basic reproduction number R-0 < 1 and an unstable equilibrium occurs for R-0 > 1. Moreover, the endemic equilibrium is stable both locally and globally when R-0 > 1. We show the global stability of an endemic equilibrium by a geometric approach. Further, numerical results are presented to validate the theoretical results. Finally, we conclude our work with a brief discussion.
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