考虑媒体报道影响的时滞结核病模型
Time-Delay Tuberculosis Model Considering the Influence of Media Reports
DOI: 10.12677/aam.2026.154186, PDF,    科研立项经费支持
作者: 耿硕涵, 魏子涵, 王光庆, 李金辉*：阜阳师范大学数学与统计学院，安徽 阜阳
关键词: 媒体报道；基本再生数；时滞；稳定性；Media Reports； Basic Reproduction Number； Time Delay； Stability
摘要: 本文建立了考虑媒体报道影响的时滞结核病模型。首先，计算出无病平衡点，使用下一代矩阵法确定了基本再生数，并分析了无病平衡点的局部和全局稳定性。其次，探讨了地方病平衡点的存在性，给出了多种存在情形，并利用Hurwitz准则分析了其稳定性。再次，通过分析特征方程的纯虚根，证明了Hopf分支的存在性，得到了模型发生Hopf分支的条件。最后，通过数值分析，验证了理论的正确性。
Abstract: In this paper, a time-delay tuberculosis model considering the influence of media reports is established. First, the disease-free equilibrium is calculated, the basic reproduction number is determined by using the next generation matrix method, and the local and global stabilities of the disease-free equilibrium are analyzed. Second, the existence of the endemic equilibrium is explored, various existence cases are given, and its stability is analyzed by using the Hurwitz criterion. Third, by analyzing the pure imaginary roots of the characteristic equation, the existence of the Hopf bifurcation is proved, and the conditions for the model to undergo Hopf bifurcation are obtained. Finally, through numerical analysis, the correctness of the theory is verified.
文章引用：耿硕涵, 魏子涵, 王光庆, 李金辉. 考虑媒体报道影响的时滞结核病模型[J]. 应用数学进展, 2026, 15(4): 596-608. https://doi.org/10.12677/aam.2026.154186

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