接触率作为流行指数函数的SEIR模型的全局稳定性

Global Stability of the SEIR Model with Contact Rate as a Function of Prevalence Index

考虑了一个包含接触方式变化信息的SEIR流行病模型,给出了基本再生数R_(0),求解了两类平衡点。应用Lyapunov函数的方法证明了当R_(0)<1时,无病平衡点在可行域内是全局渐近稳定的;当R_(0)>1时,在特定条件下,地方病平衡点在可行域内是全局渐近稳定的。通过对研究的流行病模型进行数值模拟,发现提高潜伏期患者的治愈率和降低治疗失败的比例,可以有效缩短疾病消亡或趋于稳定的时间,即可以有效控制疾病的传播。

In this paper,we consider an SEIR epidemiological model with information-related changes in contact patterns,give the basic reproduction number R_(0) and solve two kinds of equilibrium points.The method of Lyapunov function is used to prove that when R_(0)<1,the disease-free equilibrium point is globally asymptotically stable in the feasible region and when R_(0)>1,it is proved that the endemic equilibrium point is globally asymptotically stable under certain condition in the feasible region.Through numerical simulation of the epidemiological model,it’s found that increasing the cure rate of the exposed people and reducing the proportion of treatment failure can effectively shorten the time of death or stabilization of the disease,and effectively control the spread of the disease.