现实复杂情形下的SIRS型传染病模型及其控制策略_孙有发现实复杂情形下的SIRS型传染病模型及其控制策略_孙有发.pdfVIP

第22 卷第1 期 系 统 仿 真 学 报© Vol. 22 No. 1 2010 年1 月 Journal of System Simulation Jan., 2010 现实复杂情形下的SIRS型传染病模型及其控制策略 1 1 1 1 2 孙有发 ，郭旭冲 ，梁肖肖 ，刘彩燕 ，张成科 (1.广东工业大学管理学院，广州 510520 ；2.广东工业大学经济与贸易学院，广州 510520) 摘 要：研究现实复杂情形下( 包含非线性传染率、有隔离措施、群外个体迁入、生育与死亡以及 疾病可水平和垂直传播等)的 SIRS 型传染病模型。首先证明该传染病模型的无病平衡点与地方病 平衡点的唯一存在性及渐近稳定性；然后从基本再生数以及折衷考虑人道主义、救治代价与疾病 控制效果的原则，针对流行于人类的传染病，提出 “优先隔离染病个体、提高疾病治愈率以及控 制传染病垂直传播”的传染病综合控制策略；最后，数值仿真验证了模型的稳态特性以及综合控制 策略的有效性。 关键词：传染病模型；SIRS；隔离；迁入；垂直传播；控制策略 中图分类号: TP391.9 ；Q-332 文献标识码: A 文章编号: 1004-731X (2010) 01-0195-06 SIRS Epidemic Model under Real Complex Circumstances and Its Control Strategy 1 1 1 1 2 SUN You-fa , GUO Xu-chong , LIANG Xiao-xiao , LIU Cai-yan , ZHANG Cheng-ke (1. School of Management, Guangdong University of Technology, Guangzhou 510520, China; 2. School of Economic and Trade, Guangdong University of Technology, Guangzhou 510520, China) Abstract: An SIRS infectious disease model under such real complex circumstances that the transmission rate of disease is non-linear; quarantine measures were partially taken for infectious individuals; immigrations, fertility and death of individuals were permitted; and finally diseases could be both directly and vertically transmitted, was studied. The disease-free and epidemic equilibriums were calculated and proved to be asymptotically stable with certain conditions . Acco