考虑医院病床数的SIR模型的分支分析

Bifurcations of an SIR Epidemic Model with the Impact of the Number of Hospital Beds

建立了具有标准发生率且考虑医院病床数的SIR模型,并对其性态进行了分析.通过分析,发现R_0不再是疾病流行的阈值,并且当医院的病床数小到一定值时模型就会出现后向分支和鞍结点分支.通过数值模拟可以看出当病床数b减少时,模型会呈现出一系列复杂的动力学性态,如:Hopf分支,BT分支和同宿轨分支.通过对模型的研究与分析可以看出医院的病床数是一个极其重要的因素,当R0<1时,通过增加医院的病床数是可以消灭疾病的;当R_0>1时通过增加病床数可以使得疾病得到控制不会出现一些复杂的发展趋势.

In this paper, we establish and study an SIR model with a standard incidence rate and a nonlinear recovery rate defined as a function of the number of the beds and infected. For the model, we find that the reproduction number R0 is not a threshold parameter and when the number of the beds is low, the model undergoes Backward bifurcation. By numerical simulation, it is shown that model undergoes Hopf bifurcation, Bogdanov-Taken bifurcation and Homoclinic bifurcation when the number of the beds is too small. By simulation and analysis, we find that the number of the beds is a important factor, when R0 〈 1, the epidemic can be eliminated by increasing the number of the beds; when R0 〉 1, the epidemic can be controlled by the same method.