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

Modeling and Behavior Analysis of an Epidemic Model with Latency and the Impact of Medical Resource

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R_0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R_0<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.

In this paper, an epidemic model with latency is explored in order to understand how the medical resources efficiency affect the transmission of infectious disease, whilst the dynamic behaviors of the model is investigated. It is shown that the outcome of disease spread may depend on both the basic reproduction number R0 and the number of hospital beds. The critical threshold value of hospital beds is obtained. If the basic reproduction number Ro is greater than 1, there exists a unique endemic equilibrium and we prove that it is globally stable by constructing a Dulac function. If R0 〈 1, we obtain the existence conditions for endemic equilibria, in addition, the model undergoes backward bifurcation when Ro 〈 1 and the number of beds is less than the critical threshold value. According to the actual situation to make sure the number of hospital beds is no less than the critical threshold value, it is not only be contribute to control the disease but also prevent the excessive medical resources from leading to resources-wasting.