Research Article Open Access

On Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS Disease

S. A.A. El-Marouf1
  • 1 Department of Mathematics, Faculty of Science, Taibah University, Madinahmonwarah, Saudi Arabia

Abstract

Problem statement: This study aims to discuss the stability and bifurcation of a system of ordinary differential equations expressing a general nonlinear model of HIV/AIDS which has great interests from scientists and researchers on mathematics, biology, medicine and education. The existance of equilibrium points and their local stability are studied for HIV/AIDS model with two forms of the incidence rates. Conclusion/Recommendations: A comparison with recent published results is given. Hopf bifurcation of solutions of an epidemic model with a general nonlinear incidence rate is established. It is also proved that the system undergoes a series of Bogdanov-Takens bifurcation, i.e., saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation for suitable values of the parameters.

American Journal of Applied Sciences
Volume 9 No. 7, 2012, 961-967

DOI: https://doi.org/10.3844/ajassp.2012.961.967

Submitted On: 11 January 2012 Published On: 24 April 2012

How to Cite: El-Marouf, S. A. (2012). On Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS Disease. American Journal of Applied Sciences, 9(7), 961-967. https://doi.org/10.3844/ajassp.2012.961.967

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Keywords

  • Epedimic models
  • infectious disease
  • HIV/AIDS model
  • local stability
  • hopf bifurcation
  • bogdanov-takens bifurcation