具有急慢性期的丙肝SICRS模型全局动力学分析

Global Dynamics Analysis of Hepatitis C SICRS Model with Acute and Chronic Stage

丙型肝炎病毒(hepatitis C virus,HCV)感染可引发严重的肝脏疾病,对人类健康危害极大,已经成为严重的公共卫生问题.为了研究HCV的传播机理,建立了一个具有急、慢性期和免疫失效的丙肝传染的SICRS模型.首先,直接计算得到了模型无病平衡点、地方病平衡点的存在性和模型的基本再生数R.其次,通过构造适当的Lyapunov函数证明了无病平衡点和地方病平衡点的稳定性,即当R_(0)≤1时无病平衡点全局渐近稳定,当R>1时在一定条件下地方病平衡点全局渐近稳定.最后,对参数免疫失效率、急性患者传染率以及治疗率进行了数值模拟,并根据数值模拟结果对丙肝的预防和控制提出了可行性建议.

Hepatitis C virus(HCV) infection can cause serious liver disease.It is very harmful to human health and has become a serious public health problem.In order to study the transmission mechanism of HCV,a hepatitis C SICRS model with acute and chronic phase and immune failure is established.Firstly,the existence of the disease-free equilibrium endemic equilibrium of the model are calculated directly and the basic reproductive number Ris obtained.Then,by constructing appropriate Lyapunov functions,the stability of disease-free equilibrium and endemic equilibrium is proved,that is,the disease-free equilibrium is globally asymptotically stable if R_(0)≤1,and the endemic equilibrium is globally asymptotically stable under certain conditions if R>1.Finally,the parameter immune failure rate,acute patient infection rate and treatment rate are numerically simulated,and feasible suggestions for the prevention and control of hepatitis C are put forward according to the numerical simulation results.