摘要
研究了具有非线性发生率的SIR传染病模型.该发生率满足一定条件.通过对模型的分析,发现模型参数在满足某些值时,模型会发生后向分支现象.此时R0=1不能作为疾病是否消亡的阈值条件.在拐点处的临界值被作为新的阈值.分析了模型发生后向分支的条件,得到了无病平衡点和地方病平衡点稳定的充分条件.主要结论均通过数值模拟加以验证.
An SIR epidemic model with non-linear incidence rate which subject to a few general conditions is investigated. It is found that the backfoward bifurcation occurs for the model if some parameters are specific values. To drive the basic reproduction number less than the unity is not enough to eradicate the disease, and the critical value at the turning point becomes a new threshold. Some sufficient conditions for the disease-free equilibrium and the endemic equilibrium being stable are also obtained. The main results are illustrated by numerical simulations.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2012年第4期353-357,共5页
Journal of North University of China(Natural Science Edition)
基金
国家自然科学基金(60771026)
山西省青年科技基金(2007021006)
关键词
非线性发生率
SIR模型
后向分支
平衡点
稳定性
nonlinear incidence rate
SIR model
backward bifurcation
equilibria
stability
