考虑潜伏期及医疗资源影响的SEIS模型动力学分析

Behavior analysis of an SEIS epidemic model with latency and the impact of medical resource

建立并分析考虑潜伏期及医疗资源影响的SEIS模型,其中医疗资源的影响主要考虑医院病床的数量与恢复率的关系。分析模型发现:当基本再生数R0>1时,系统只存在唯一正平衡点;当R0<1时,系统可能存在两个或无正平衡点,并且当医院的病床数小到一定值时,系统会发生后向分支,因此可以找到病床的存在阈值,这样既不造成浪费,又能保证治疗疾病时具有充足的资源。

An SEIS model, in which the latency and the impact of medical resource are considered, is investigated and analyzed. The impact of medical resource is on the relationship between the number of hospital beds and the recovery rate. For the model, it is found that if the basic reproduction number Ro is greater than 1, there exists a unique endemic equilibrium; if R0 〈 1 , there may exist two or no endemic equilibrium. In addition, the model undergoes backward bifurcation when the number of hospital beds is less than a certain value. Therefore, the critical threshold of hospital beds can be found, which is not on- ly low-cost but also can ensure the treatment of disease with sufficient resources.