| 引用本文: | 曹宇,井元伟.带有非线性感染率的SIRS模型的建立与稳定性分析[J].控制理论与应用,2013,30(2):229~232.[点击复制] |
| CAO Yu,JING Yuan-wei.Modeling and stability analysis for SIRS model with nonlinear infection rate[J].Control Theory and Technology,2013,30(2):229~232.[点击复制] |
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| 带有非线性感染率的SIRS模型的建立与稳定性分析 |
| Modeling and stability analysis for SIRS model with nonlinear infection rate |
| 摘要点击 3960 全文点击 1490 投稿时间：2012-04-17 修订日期：2012-07-26 |
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| DOI编号 10.7641/CTA.2013.20369 |
| 2013,30(2):229-232 |
| 中文关键词 复杂网络 非线性感染率 SIRS模型 阈值条件 |
| 英文关键词 complex networks nonlinear incidence rate SIRS epidemic model threshold condition |
| 基金项目 国家杰出青年科学基金资助项目(51685168); 教育部重点科研基金资助项目(02152); 中央高校基本科研业务费(N110804005). |
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| 中文摘要 |
| 针对以往SIRS(易感–感染–免疫–易感)模型中没有考虑到感染率取值范围的情况, 提出了一种带有非线性感染率的SIRS改进模型, 从理论上限制了感染率的取值范围; 利用平均场理论分析得到了病毒在均匀网络和无标度网络中的传播阈值及阈值条件; 利用李雅普诺夫稳定性理论分析了系统在平衡点处的稳定性并得到了病毒传播过程不仅受到网络拓扑结构的影响还与感染概率, 免疫概率有密切关系. |
| 英文摘要 |
| To improve the existing SIRS (susceptible-infected-recovered-susceptible) model in which the infection rate is not considered, we propose an improved model by taking into account additionally the probability of infection range. The threshold and threshold conditions are derived based on the main-field theory on uniform networks and scale-free networks. We analyze the stability of the system near the equilibrium point by using Lyapunov stability theory and obtain the conclusion that the virus transmission process is not only related to the topology of networks but also on the infection probability and the immunity probability. |