具有复杂脉冲效应的SIS传染病模型的周期解  

Periodic solutions of an SIS epidemic model with complex pulse effects

作　　者：于佳佳 蒋贵荣[1] 邓国强[1] 凌琳[1] YU Jiajia;JIANG Guirong;DENG Guoqiang;IANG Lin(School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2018年第3期233-237,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11662001;11562006;11771105);广西自然科学重点基金(2016GXNSFDA380031);广西自然科学杰出青年基金(2017GXNSFFA198012);桂林电子科技大学研究生教育创新计划(2017YJCX81)

摘　　要：针对经典传染病模型只考虑一种脉冲效应的问题,建立一类带有标准发生率的SIS传染病模型,并且考虑脉冲生育和脉冲治疗2种脉冲效应。利用离散映射以及脉冲动力系统理论,得到无病周期解存在和稳定的充分条件,以及地方病周期解存在的充分条件。数值模拟验证了充分条件的合理性。In view of the situations in classic infectious disease model have single pulse effect.A class of SIS epidemic model with fixed-time birth pulse,state pulse treatment,and standard incidence is built in this paper.The sufficient conditions for existence and stability of disease free periodic solution and endemic periodic solution are obtained by using discrete mapping and the theory of impulsive dynamical system.Numerical simulations on periodic solutions are shown by the illustrative examples.

关 键 词：SIS传染病模型 生育脉冲 脉冲治疗 标准发生率 

分 类 号：O175.1[理学—数学]