Global dynamics of SEIRS epidemic model with non-linear generalized incidences and preventive vaccination

• Main Authors: Khan, Muhammad Altaf, Badshah, Qaisar, Islam, Saeed, Khan, Ilyas, Shafie, Sharidan, Khan, Sher Afzal
• Format: Article
• Published: Springer 2015
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/55486/; http://dx.doi.org/10.1186/s13662-015-0429-3
• Institution: Universiti Teknologi Malaysia

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 (Formula Presented.) and an unstable equilibrium occurs for (Formula Presented.). Moreover, the endemic equilibrium is stable both locally and globally when (Formula Presented.). 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