On Stability and Bifurcation of Solutions ofNonlinear System of Differential Equations for AIDS Disease | Science Publications

American Journal of Applied Sciences

S. A.A. El-Marouf¹ 

关键词: local stability;    hopf bifurcation;    bogdanov-takens bifurcation;    Epedimic models;    infectious disease;    HIV/AIDS model;   

DOI  :  10.3844/ajassp.2012.961.967

学科分类：自然科学（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown