一类带有周期传染率的百日咳传染病模型  

A pertussis epidemic model with periodic infection rate

作　　者：南希 刘俊利[1] NAN Xi;LIU Junli(School of Science,Xi′an Polytechnic University,Xi′an 710048,China)

机构地区：[1]西安工程大学理学院

出　　处：《纺织高校基础科学学报》2019年第4期398-403,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11801431,11801432);陕西省自然科学基础研究计划项目(2018JM1011)

摘　　要：针对百日咳疾病的流行随时间呈周期性变化的特点,在具有二次感染的S1I1RVS2I2百日咳模型基础上考虑带有周期传染率的百日咳传染病模型。利用积分算子的谱半径得到了模型的基本再生数R0,R0决定了百日咳传染病的灭绝和一致持久性。通过Poincare映射,讨论了模型的一致持续生存。通过数值模拟验证了:当R0=0.2526<1时,百日咳传染病模型的无病平衡点是局部渐近稳定的,疾病绝灭;当R0=4.4273>1时,无病平衡点不稳定,疾病持续存在,且模型还存在正周期解。Due to the periodicity of pertussis prevalence,based on the S 1I 1RVS 2I 2 pertussis model with secondary infection,a pertussis infectious disease model with periodic infection rate was considered.Using the spectral radius of the integral operator,the basic reproduction number R 0 was obtained.R 0 determines the extinction and uniform persistence of pertussis.The uniform persistence of the model was discussed by Poincare map.The theoretical results are verified by numerical simulations.It shows that when R 0=0.2526<1 the disease-free equilibrium of the model is locally asymptotically stable and the disease dies out;when R 0=4.4273>1,the disease-free equilibrium is unstable and the disease persists.The model also has a positive periodic solution.

关 键 词：百日咳模型 基本再生数 周期解 传染率 稳定性 一致持久性 

分 类 号：O175.1[理学—数学]