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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Global Analysis of an Epidemic Model with Non-Linear Incidence Rate

S. A.A. El-Marouf and S. M. Alihaby

Abstract

Problem statement: In this study the equilibrium points and their local stability are found for SIQ and SIQR epidemic models with three forms of the incidence rates. Also, we study the global stability of the equilibrium by constructing the new forms of Liapounov functions. Conclusion/Recommendations: We explored the existence of Hopf bifurcation for some parameters in the given model.

Journal of Mathematics and Statistics
Volume 7 No. 4, 2011, 319-325

DOI: https://doi.org/10.3844/jmssp.2011.319.325

Submitted On: 25 September 2011 Published On: 28 October 2011

How to Cite: El-Marouf, S. A. & Alihaby, S. M. (2011). Global Analysis of an Epidemic Model with Non-Linear Incidence Rate. Journal of Mathematics and Statistics, 7(4), 319-325. https://doi.org/10.3844/jmssp.2011.319.325

Open AccessCopyright: © 2011 S. A.A. El-Marouf and S. M. Alihaby. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Epidemic models
  • infectious disease
  • endemic model
  • local stability
  • global stability
  • hop bifurcation
  • quarantined individuals
  • infected individuals
  • periodic solutions