TY  - JOUR
AU  - El-Marouf, S. A.A. 
PY  - 2012
TI  - On Stability and Bifurcation of Solutions of  Nonlinear System of Differential Equations for AIDS Disease
JF  - American Journal of Applied Sciences
VL  - 9
IS  - 7
DO  - 10.3844/ajassp.2012.961.967
UR  - https://thescipub.com/abstract/ajassp.2012.961.967
AB  - 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.