一类带有治疗的乙肝病毒动力学模型的稳定性和Hopf分支

Stability and Hopf bifurcation for a hepatitis B virus dynamics model with drug therapy

建立了一类具有Logistic增长和治疗的乙肝病毒动力学模型,分析确定了疾病是否流行的阈值0R.当0R<1时,证明了无病平衡点是全局渐近稳定的,疾病消亡;当0R>1时,运用稳定性和分支理论,证明了系统可能出现Hopf分支.数值模拟验证了理论结果.

Formulated and analyzed a hepatitis B virus dynamics model with Logistic hepatitis growth and drug therapy. Obtained the basic reproduction number R0 , which determines the disease is epidemic or not. Proved that the disease-free equilibrium is globally asymptotically stable and the infection becomes extinct if R0 〈 1. When R0 〉 1, using theories of stability and bifurcation, it was proved that a Hopf bifurcation may occur. Finally, numerical simulations were presented to verify the theoretical analysis.