媒体报道对传染病传播影响的平面Filippov系统
The Planar Filippov System Examining the Impact of Media Reports on Infectious Disease Transmission
摘要: 考虑到媒体报道对 SIR 传染病传播的影响是不连续的具有间歇性. 本文建立了一类采取闹值策略 的 Filippov 传染病模型, 利用 Filippov 意义下的右端不连续微分方程理论, 对 SIR 传染病模型 在闹值策略下进行了定性分析. 研究了 Filippov 传染病模型的滑模动力学和全局动力学, 并得到 了滑模域、 伪平衡点存在性以及平衡点 (无病平衡点、 地方病平衡点和伪平衡点) 全局渐近稳定的 充要条件. 同时也可说明适当的媒体报道能够减少感染者的数量, 使感染者的数量低于闹值.
Abstract: A Filippov SIR epidemic model with a threshold strategy is developed to capture the discontinuous and intermittent impact of media coverage. Using Filippov’s theory of differential equations with discontinuous right-hand sides, this study qualitatively analyzes the model, examining its sliding mode and global dynamics. It establishes necessary and sufficient conditions for the existence of the sliding domain and a pseudo -equilibrium, as well as for the global asymptotic stability of the disease-free, endemic, and pseudo-equilibria. The findings indicate that appropriate media coverage can effectively contain the infected population below a threshold level.
文章引用：盛艳红. 媒体报道对传染病传播影响的平面Filippov系统[J]. 应用数学进展, 2026, 15(3): 463-477. https://doi.org/10.12677/AAM.2026.153119

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