媒体报道诱导的离散传染病切换系统建模与分析

Modeling and Analysis of a Discrete Switched Epidemic System Induced by Media Reports

  • 摘要: 针对疾病数据收集单位不连续的情况, 运用Euler离散法建立了一类由媒体报道诱导的离散SIR传染病切换模型。从理论上研究了切换系统子系统地方病平衡点的存在性、稳定性等动力学行为。从数值上研究了切换系统的平衡点分支、单参数分支、初值敏感性。研究发现: 关键参数的小扰动直接影响着疾病的暴发次数与频率, 同时媒体报道可以降低疾病传染率, 有效遏制疾病的流行与暴发。

     

    Abstract: In view of the discontinuity of disease data collection units, Euler discrete method is used to establish a kind of discrete SIR infectious disease switching model induced by media reports.The existence and stability of the endemic equilibria of two subsystems are studied theoretically. By numerical simulation, the equilibria bifurcation, sensitivity analysis of the key parameter and initial value are investigated. The results show that the minor perturbation of some parameters can influence the frequency and times of the outbreak of the infectious disease. Meanwhile, the disease transmission rate can be reduced through media reports, and the outbreak of the disease can be prevented effectively.

     

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