具瞬时脉冲接种与非瞬时脉冲接种效应的一类新的SIR传染病模型研究  

DYNAMICS OF A NEW SIR EPIDEMIC MODEL WITH TRANSIENT/NON-TRANSIENT IMPULSIVE VACCINATION EFFECTS

作　　者：汪袁 焦建军 全琦 WANG Yuan;JIAO Jian-jun;QUAN Qi(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guizhou 550025,China;School of Mathematical Sciences,Guizhou Normal University,Guizhou 550025,China)

机构地区：[1]贵州财经大学数统学院,贵州贵阳550025 [2]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《数学杂志》2022年第4期367-376,共10页Journal of Mathematics

基　　金：国家自然科学基金资助(11791019);贵州省微分-差分动力系统应用科技创新人才团队项目基金资助(20175658);贵州省高层次创新型人才(百层次)项目基金资助(20164035);贵州省教育厅创新群体重大项目基金资助(2018019)。

摘　　要：本文研究了瞬时脉冲接种与非瞬时脉冲接种效应的SIR传染病模型的问题.利用频闪映射和Floquet定理以及脉冲微分方程理论的方法,获得了模型无病周期解的存在性和疫苗接种的控制阈值的结果,推广了瞬时脉冲接种率与非瞬时脉冲接种区间长度对疾病灭绝起着重要作用的结论,为实际传染病控制提供了可靠的策略支持.In this paper,we study the problem of epidemic model with transient/nontransient impulsive vaccination effects.Using the theories of stroboscopic map,Floquet and the theories of impulsive differential equations,we obtain the existence of infection-free periodic solution and the controlling thresholds of the vaccination.The results show that the transient impulsive vaccination rate and the length of non-transient impulsive vaccination effect interval played an important role in disease extinction.It provides a reliable strategy support for practical vaccination.

关 键 词：脉冲接种 非瞬时脉冲接种区间长度 疾病消除 

分 类 号：O175.13[理学—数学]