一类具有饱和发生率和治疗的SIS传染病模型的后向分支及动力学行为

Backward Bifurcation and Dynamical Behaviors of an SIS Epidemic Model with Saturated Incidence Rate and Treatment

研究了一类具有饱和发生率和治疗的SIS传染病模型的平衡点的后向分支和动力学性质.假定在治疗能力之内时治疗率是与染病者的数量成比例的,当染病者的数量超过了治疗能力承受的界限时,治疗函数为某一常数形式.研究发现,如果治疗能力较小时,模型将出现后向分支现象,分析的结果表明仅靠降低基本再生数到1以下并不一定能够使疾病根除.

In this paper, backward bifurcation and dynamical behaviors of an SIS epidemic model with saturated incidence rate and treatment is investigated.It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity.It is found that a backward bifurcation occurs if the capacity is small.Theoretical and numerical results suggest that decreasing the basic reproduction number below one only is insuffcient for disease eradication.