关于一类具有垂直传染与治疗SIR模型产生后向分支的研究  

Backward bifurcation of an SIR epidemic model with treatment and vertical transmission

作　　者：段西超[1] 杨艳华[2] 

机构地区：[1]空军第一航空学院基础部,河南信阳464000 [2]信阳农业高等专科学校计算机科学系,河南信阳464000

出　　处：《河南科技学院学报（自然科学版）》2011年第5期47-50,共4页Journal of Henan Institute of Science and Technology(Natural Science Edition)

摘　　要：考虑了有限治疗资源和垂直传染的一类传染病模型,当染病个体数量小于某确定值时,治疗康复人数与染病个体数成比例;当染病个体数量大于某确定值时,治疗康复人数是确定常数值.确定了模型的基本再生数R0.在一定条件下,当R0>1时,地方病平衡点E*是渐进稳定的;当R0<1时,后向分支就产生了.An epidemic model that incorporates a limited resource for treatment and vertical transmission have been considered.The total host population is assumed to have constant density.It is assumed that treatment rate is proportional to the number of infectivities below the capacity and is a constant when the number of infectivities is greater than the capacity.The basic reproduction number of the disease R0 is found.If R01 the endemic equilibrium E＊ is asymptotically stable under some conditions.If R01 a backward bifurcation occurs.

关 键 词：传染病 后向分支 治疗 垂直传染 

分 类 号：Q332[生物学—遗传学]