基于差分方程理论研究一类离散时间的SEIS传染病模型

Research on a discrete-time SEIS epidemic model based on the difference equations theory

运用差分方程的稳定性理论分析了一类离散时间的SEIS传染病模型,该模型是基于欧拉向前差分的方法,对连续时间的模型离散化得到的.首先,给出了模型所有解的正则性和有界性,以及模型平衡点的存在;其次,利用Jury判据和离散的Lyapunov函数法,证明了当R_0<1时无病平衡点P_0的局部和全局渐近稳定性;最后,借助MATLAB软件的数值模拟,讨论了当R_0>1时地方病平衡点P1可能是全局渐近稳定的.

This paper analyses a discrete SEIS epidemic model derived from the continuous-time model by using the forward Euler method,which is used the stability theory of the difference equations.Firstly,we give out that the positivity and boundedness of all solutions,and the existence of the equilibrium.Then,by the Jury criterion and the discrete Lyapunov function method,we prove that the disease-free equilibrium P0 is locally and globally asymptotically stable if R0 〈1.Finally,with the help of numerical simulations in MATLAB software,we discuss that the endemic equilibrium P1 is likely globally asymptotically stable if R0 〉 1.