一类具有非线性传染率SEIS模型的定性分析  

Qualitative Analysis of an SEIS Model with Nonlinear Incidence Rates

作　　者：徐雪璇 赵建东 XU Xuexuan;ZHAO Jiandong(School of Mathematics and Statistics Science,Ludong University,Yantai 264039,China)

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264039

出　　处：《鲁东大学学报（自然科学版）》2021年第3期200-206,共7页Journal of Ludong University:Natural Science Edition

基　　金：山东省自然科学基金(ZR2018AM045)。

摘　　要：考虑出生率和死亡率不同,建立具有非线性传染率的SEIS传染病模型,讨论此模型正平衡点的存在性和模型无病平衡点的局部稳定性。根据Routh-Hurwitz判据得到正平衡点局部稳定的充要条件,并利用Lyapunov函数给出无病平衡点和正平衡点全局渐近稳定的充分条件。最后,用数值模拟说明主要结果的正确性。Considering the difference of the birth rate and death rate,an SIES model with incidencerates was proposed.At first,the existence of the positive equilibria was discussed,then the local stability of the disease-free equilibrium was analyzed,and the sufficient and necessary conditions for the local stability of the positive equilibria were obtained by Routh-Hurwitz criterion.Furthermore,the sufficient conditions for the globally asymptotic stability of the disease-free equilibrium and the positive equilibria were given by using Lyapunov function.Finally,the main results were illustrated by some simulations.

关 键 词：SEIS模型 非线性传染率 平衡点 稳定性 

分 类 号：O175.1[理学—数学]