基于SIRS传染病模型的不同控制策略比较  

Comparison of Different Control Strategies Based on a SIRS Epidemic Model

作　　者：赵明[1] 

机构地区：[1]北华大学数学与统计学院,吉林吉林132033

出　　处：《北华大学学报（自然科学版）》2015年第5期561-566,共6页Journal of Beihua University（Natural Science）

基　　金：吉林省教育厅科学技术研究项目(2015157)

摘　　要：建立并分析了一类具有标准发生率、垂直传染、连续接种和治疗的SIRS传染病模型.综合运用RouthHurwitz判据、La Salle不变集原理和广义Bendixson-Dulac定理,获得了保证SIRS传染病模型的无病平衡点和地方病平衡点全局渐近稳定的阈值条件.通过比较两种控制策略的有效性,说明同时使用接种和治疗两种策略比单独应用一种更有效.A SIRS epidemic model with standard incidence rate, vertical transmission, continuous vaccination and treatment is established and analyzed. By using Routh-Hurwitz criterion, LaSalle invariant set principle and generalized Bendixson-Dulac theorem, the global asymptotic stable threshold conditions of disease-free equilibrium and endemic equilibrium in the SIRS epidemic model are obtained. Comparing the effectiveness of the two control strategies shows that using two strategies of vaccination and treatment concurrently is superior to only one strategy for eradicating the disease.

关 键 词：SIRS传染病模型 连续接种和治疗 无病平衡点 地方病平衡点 全局稳定性 

分 类 号：O175.1[理学—数学]