具有接种项且考虑医院病床数的SVIS模型的性态分析  

Dynamic behavior of an SVIS epidemic model with vaccination and the impact of the number of hospital beds

作　　者：张永鑫[1] 李桂花[1] 康彩丽[1] 

机构地区：[1]中北大学理学院,太原030051

出　　处：《黑龙江大学自然科学学报》2016年第5期606-610,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11201434);山西省留学回国人员科技活动择优资助项目

摘　　要：建立具有接种项且考虑医院病床数的SVIS模型,并对其动力学性态进行了分析。发现:基本再生数R_0是疫苗接种率φ的函数,并且当传染率较大或者病床数目较小时,系统会出现后向分支,即当R_0小于1时,系统会出现两个正平衡点或者无正平衡点;当系统存在两个正平衡点时,其中染病者数量较小的是鞍点,染病者数量较大的为非鞍点。当R_0小于1时,通过增加病床数和减少疾病的传染率,可以消除疾病。An SVIS model with vaccination and the impact of the number of hospital beds is established, its dynamic behavior is studied. For the model, it is found that the basic reproduction number R0 is a function of the vaccination φ, and the system undergoes backward bifurcation if the incidence rate is big or the number of beds is small, i.e. , when R0 〈 1 there exist two positive equilibria or none in the model. If there exist two positive equilibria, then the lower infected one is a hyperbolic saddle, and the higher one is an anti-saddle. The epidemic can be eliminated by increasing the number of beds or decreasing the value of incidence rate when R0 〈 1 .

关 键 词：接种项 SVIS模型 医院病床数 后向分支 

分 类 号：O175.1[理学—数学]