对慢性感染者进行治疗的丙肝SICTR模型的全局性态分析

Global behavior analysis of SICTR model of hepatitis C treated with chronic infection

为了进一步研究丙型肝炎病毒的传播机理及其治疗的有效性,考虑了丙肝感染的急性期和慢性期阶段,建立了一个对慢性感染者进行治疗的丙肝SICTR模型。首先,分析得到了疾病是否传播的阈值——基本再生数R_(0);接着,研究了模型的动力学行为,得到了模型平衡点的存在性,并通过构造适当的Lyapunov函数,证明了平衡点的稳定性,即当R_(0)<1时,无病平衡点E_(0)是全局渐近稳定的,当R_(0)>1时,地方病平衡点E^(*)在一定条件下是全局渐近稳定的;最后,数值模拟验证支持了理论结果,而且数值分析了参数的敏感性,给出了控制丙肝的有效对策。

In order to further study the transmission mechanism of hepatitis C virus(HCV)and the effectiveness of treatment,a SICTR model of HCV with treatment of chronic infection is established based on the consideration of the acute and chronic stages of HCV.Firstly,the basic reproduction number R_(0) which is the threshold for whether the disease is transmitted is obtained.Then,the dynamic behavior of the model is studied,the existence of the equilibria is obtained,and the stability of the equilibria is proved by constructing appropriate Lyapunov functions.That is,when R_(0)<1,the disease-free equilibrium E_(0) is globally asymptotically stable,and when R_(0)>1,the endemic equilibrium E^(*) is globally asymptotically stable under certain conditions.Finally,the numerical simulation is used to verify the correctness of the theory results.The sensitivity of parameters is numerically analyzed,and the method to control HCV is given.