一类含有脉冲免疫和治疗的SIR流行病的分析  

Analysis of a Nonlinear SIR Epidemic Model with Pulse Vaccination and Treatment

作　　者：朱芳芳 唐雪凝 孟新柱 ZHU Fang-fang;TANG Xue-ning;MENG Xin-zhu(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao Shandong 266590,China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《大学数学》2018年第1期7-12,共6页College Mathematics

基　　金：国家自然科学基金(11371230);山东省自然科学基金(ZR2015AQ001)

摘　　要：在考虑脉冲接种和脉冲治疗的基础上,本文提出了一类新的含有两个脉冲过程和治疗的SIR传染病模型.利用频闪映射和Floquet理论,研究了无病周期解的存在性与稳定性,这意味着疫情最终可能灭绝.此外,研究了该流行病持久流行的条件,获得了决定疫情是否发生的基本再生数.最后,通过数值模拟分析,说明了脉冲接种和脉冲治疗对疾病控制的影响.This paper proposes a novel SIR epidemic model with twice pulse process which considers the pulse vaccination and pulse treatment.By using stroboscopic map and Floquet theory,we investigate the existence and local stability of the disease free periodic solution,which implies the epidemic disease may go to extinction ultimately.In addition,we show that the disease may be persistent and epidemic under some conditions,and we obtain the basic reproduction number which determines whether or not epidemics occur.Finally,numerical simulation analysis is applied to illustrate the influences of pulse vaccination and pulse treatment on disease control.

关 键 词：SIR传染病模型 脉冲接种 脉冲治疗 饱和传染率 

分 类 号：O175[理学—数学]