网络上具有一般直接免疫的SIRS传染病模型分析 |
| |
引用本文: | 张斐,吴庆初,曾广洪.网络上具有一般直接免疫的SIRS传染病模型分析[J].复杂系统与复杂性科学,2017,14(1). |
| |
作者姓名: | 张斐 吴庆初 曾广洪 |
| |
作者单位: | 江西师范大学数学与信息科学学院,南昌,330022 |
| |
基金项目: | 国家自然科学基金,江西省自然科学基金 |
| |
摘 要: | 考虑复杂网络上具有一般直接免疫率的SIRS传染病模型。由地方病平衡点的存在性,确定了传染病的流行阈值λc,并且通过构造合适的李雅普诺夫函数证明:当λ≤λ_c时,无病平衡点全局渐近稳定;当λλ_c时,地方病平衡点全局渐近稳定。根据免疫率的分布,提出了一致性直接免疫和目标性直接免疫。结果表明,在平均免疫率相等的条件下存在免疫丧失率的临界值δ_c,当δδ_c(δδ_c)时,目标性免疫的流行阈值小于(大于)一致性免疫的流行阈值。
|
关 键 词: | 复杂网络 SIRS模型 全局稳定性 异质免疫率 |
An Analysis of an SIRS Epidemic Model with General Direct Immunization in Networks |
| |
Authors: | ZHANG Fei WU Qingchu ZENG Guanghong |
| |
Abstract: | We consider an SIRS epidemic model with a general direct immunization rate on networks.By constructing suitable Lyapunov functions, we find that the dynamical behvaior of the model is completely determined by the epidemic threshold λc.When λ≤λc, the disease-free equilibrium is globally asymptotically stable;when λ>λc, the endemic equilibrium is globally asymptotically stable.In addition, we propose a uniform direct immunization and a targeted direct immunization.The results show that under the same average immunization rate s there exists a critical immunization-lost rate δc so that the epidemic threshold of the targeted direct immunization is smaller (larger) than that of the uniform direct immunization if δ<δc(δ>δc). |
| |
Keywords: | complex network SIRS model global stability heterogeneous immunization rate |
本文献已被 CNKI 万方数据 等数据库收录! |
|