具有饱和接触率的SIQR传染病模型的不同控制策略  

Analysis of an SIQR epidemic model with saturated contact rate and control strategies

作　　者：陈立范[1] 李维德[1] 朱玑[1] 

机构地区：[1]兰州大学数学与统计学院,兰州730000

出　　处：《兰州大学学报（自然科学版）》2012年第6期114-118,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(40930533;11126183)

摘　　要：讨论了带有隔离和不同接种策略的SIQR传染病模型.在连续接种策略下给出了无病平衡点和地方病平衡点的存在性和全局稳定性;在脉冲接种策略下,获得了无病周期解,并给出了无病周期解全局稳定的充分条件,同时也讨论了隔离率、连续接种率、脉冲接种率、治疗率等参数对疾病防治的重要性.A kind of SIQR epidemic models with isolation and different vaccination strategies was investigated and,under the continuous vaccination strategy,the existence and globally asymptotical stability of diseasefree equilibrium and endemic equilibrium were obtained.With the discrete dynamic system,the infection-free periodic solution to the impulsive epidemic system was obtained and the necessary condition for the globally asymptotical stability of the solution was given on pulse vaccination strategy（PVS）.It was also showed that different parameters have different functions in eradicating a disease.

关 键 词：SIQR传染病模型 全局稳定性 基本再生数 脉冲微分方程 

分 类 号：O175.13[理学—数学] Q141[理学—基础数学]