American Journal of Applied Sciences

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

S. A.A. El-Marouf

DOI : 10.3844/ajassp.2012.961.967

American Journal of Applied Sciences

Volume 9, Issue 7

Pages 961-967

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.

Copyright

© 2012 S. A.A. El-Marouf. 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.