医疗资源影响下具有潜伏期的一类传染病模型建立及性态分析

被引：1

作者：

董宜静

李桂花

机构：

[1] 中北大学理学院

来源：

数学的实践与认识 | 2017年 / 47卷 / 05期

关键词：

传染病模型; 医院病床数; 恢复率函数; 稳定性分析; 后向分支;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

建立了医疗资源影响下的考虑疾病具有潜伏期的一类传染病模型,并分析了模型的动力学性态.发现疾病流行与否由基本再生数和医院病床数共同决定,并得到了病床数的阈值条件.当基本再生数R0大于1时,系统只存在惟一正平衡点,且通过构造Dulac函数证明了正平衡点只要存在一定是全局渐近稳定的;当R0<1,我们得到系统存在两个正平衡点及无正平衡点的条件,且只有当医院的病床数小于阈值时,系统会经历后向分支.因此,可根据实际情况使医院病床的投入量不低于阈值条件,不仅有利于疾病的控制而且不会出现医疗资源过剩的现象.

引用

页码：165 / 170

页数：6

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