| 具有连续接种和治疗的SIRS传染病模型的全局稳定性 |
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| 引用本文： | 虞秀丽. 具有连续接种和治疗的SIRS传染病模型的全局稳定性[J]. 北华大学学报(自然科学版), 2014, 0(3): 287-290 |
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| 作者姓名： | 虞秀丽 |
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| 作者单位： | 北华大学数学与统计学院,吉林 吉林,132033 |
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| 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、LaSalle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性的阀值条件.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.
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| 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 |
Global Stability of SIRS Epidemic Model with Continuous Vaccination and Treatment |
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| YU Xiu-li. Global Stability of SIRS Epidemic Model with Continuous Vaccination and Treatment[J]. Journal of Beihua University(Natural Science), 2014, 0(3): 287-290 |
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| Authors: | YU Xiu-li |
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| Affiliation: | YU Xiu-li ( Mathematics and Statistics School of Beihua University, Jilin 132033, China) |
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| Abstract: | SIRS epidemic model with standard incidence rate, vertical transmission, continuous vaccination and continuous treatment are established and analyzed. By using Routh-Hurwitz criterion, LaSalle invariant set principle and generalized Bendixson-Dulac theorem, the threshold conditions which guarantee the global asymptotic stable disease-free equilibrium and endemic equilibrium of the SIRS epidemic model is obtained. By comparing the effectiveness of two control strategies, using vaccination and treatment concurrently is superior to only one for eradicating the disease. |
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| Keywords: | SIRS epidemic model continuous vaccination and treatment infection-free equilibrium endemic equilibrium global stability |
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