10.1007/s40096-018-0271-3

On the global stability of the endemic state in an epidemic model with vaccination

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  • Mahmood Parsamanesh*1,
  • Rahman Farnoosh2,
  1. Department of Mathematics, Faculty of Science, University of Zabol, Zabol, IR
  2. Faculty of Mathematical Sciences, Iran University of Science and Technology, Narmak, Tehran, IR
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Published in Issue 2018-11-08

How to Cite

Parsamanesh, M., & Farnoosh, R. (2018). On the global stability of the endemic state in an epidemic model with vaccination. Mathematical Sciences, 12(4 (December 2018). https://doi.org/10.1007/s40096-018-0271-3
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Abstract

Abstract This paper investigates an SIS epidemic model with variable population size including a vaccination program. Dynamics of the endemic equilibrium of the model are obtained, and it will be shown that this equilibrium exists and is locally asymptotically stable when R0>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0 > 1$$\end{document} . In this case, the disease uniformly persists, and moreover, using a geometric approach we conclude that the model is globally asymptotically stable under some conditions. Also, a numerical discussion is given to verify the theoretical results.

Keywords

  • SIS epidemic model,
  • Vaccination,
  • Endemic equilibrium,
  • Global stability,
  • Geometric approach
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