一类具有复发和潜伏期传染的SEICR丙肝模型

An SEICR hepatitis C model with relapse and latent infection

依据丙肝的传播机理,我们建立了一类潜伏期具有传染性并且考虑复发效应的SEICR丙肝模型,给出了模型的基本再生数。证明了当R_(0)<1时,无病平衡点全局渐近稳定;当R_(0)>1时,无病平衡点不稳定且地方病平衡点全局渐近稳定。选取陕西省丙肝患者病例数据,利用模型数值模拟未来几年丙肝的流行趋势。最后进行参数的敏感性分析,结果表明近几年丙肝患者还将持续增加。提高公众对丙肝的检测意识、加强免疫力可以提升丙肝患者的恢复率同时减少疾病复发的可能性,这样可以控制丙肝的进一步蔓延。

According to the transmission mechanism of hepatitis C,we establish an SEICR hepatitis C model with infectious latency and relapse effect,and give the basic reproductive number of the model.It is proved that the disease-free equilibrium is globally asymptotically stable when R_(0)<1;the diseasefree equilibrium is unstable and the endemic equilibrium is globally asymptotically stable when R_(0)>1.Choosing the case data of hepatitis C patients of Shaanxi Province,we use the model to simulate the epidemic trend of hepatitis C in the next a few years.Finally,the sensitivity analysis of parameters shows that the number of hepatitis C cases will continue to increase in recent years.Improving public awareness of hepatitis C detection and strengthening immunity can improve the recovery rate of hepatitis C patients and reduce the proportion of disease relapse,so as to control the further spread of hepatitis C.