一类具有心理效应的SIRS模型的全局分析  

Global Analysis of an SIRS Epidemic Model with Psychological Effect

作　　者：姚金辉 李桂花[1] YAO Jin-hui;LI Gui-hua(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2020年第14期288-293,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11801340);山西省自然科学基金(201901D111179);山西省留学回国人员科技活动择优资助项目。

摘　　要：建立并研究了考虑心理效应影响的非单调感染强度函数的SIRS模型.通过分析,发现当基本再生数R0<1,无病平衡点是全局渐近稳定的;当R0>1时,系统存在惟一的正平衡点,且通过构造D ul ac函数证明了正平衡点只要存在就是全局渐近稳定的.这与Cui等研究的具有相同发生率函数的SEIS模型得到的结果完全不同.因此,不同的传染病有不同的传染机制,只有寻找控制传染病最为关键的因素,才能更有效的灭绝疾病.In this paper,we established an SIRS model with a non-monotonic infection force function with psychological effect,and study dynamical behaviors of the model.When R0 <1,the disease-free equilibrium is globally asymptotically stable;when R0> 1,system exists a unique positive equilibrium,by constructing Dulac function,we prove that the positive equilibrium is globally asymptotically stable only if it exists.Cui(J.Dyn.Diff.Equat) studied an SEIS model with the same as infection force function.Our conclusion is different from their some results.Theoretical analysis shows that different infectious diseases have different mechanisms,we can effectively eliminate infectious disease as long as identify the most critical factors for controlling it.

关 键 词：SIRS模型 心理效应 全局稳定性 DULAC函数 

分 类 号：R51[医药卫生—内科学] O175[医药卫生—临床医学]