接触者追踪HIV/AIDS模型的稳定性和分岔分析

Stability and bifurcation analysis of contact tracing HIV/AIDS models

研究了一类具有接触者追踪的HIV/AIDS模型,证明了无病平衡点和内部平衡点的唯一存在性.利用下一代矩阵的方法计算基本再生数,并得出平衡点稳定性的充要条件,即当基本再生数小于1时,无病平衡点是渐近稳定的;当基本再生数大于1时,内部平衡点是渐近稳定的.结合中心流形定理,讨论模型的分岔现象,给出了系统发生跨临界分岔的生物学解释.通过使用Matlab进行数值模拟,验证了系统的稳定性.同时,结合参数的生物学意义对艾滋病病毒的控制提供了建议.

A class of HIV/AIDS model with contact tracing is studied,the unique existence of disease-free equilibria and internal equilibria is demonstrated.The basic reproduction number is calculated by the next generation matrix method,the necessary and sufficient conditions for the stability of the equilibrium point are derived,that is,when the basic reproduction number is smaller than 1,the disease-free equilibrium point is asymptotical stable.When the basic reproductive number is bigger than 1,the internal equilibrium is asymptotically stable.Combined with the center manifold theorem,the bifurcation phenomenon of the model is discussed,and the biological explanation of the transcritical bifurcation of the system is given.Finally,the stability of the system is verified by using Matlab to carry out numerical simulation.At the same time,combined with the biological significance of the parameters,some suggestions for the control of HIV are proposed.