基于双重感染机制和Logistic增长的基孔肯雅病毒动力学模型

A Chikungunya Virus Dynamic Model Incorporating Dual Infection Mechanism and Logistic Growth

摘要: 为深入理解基孔肯雅病毒的宿主体内感染机制，本文构建并分析一个包含双重感染途径的四维动力学模型。该模型整合病毒–细胞和细胞–细胞两种传播途径、易感细胞的Logistic增长以及B细胞介导的免疫应答。本文推导基本再生数$R_0$ ，并将其作为判定病毒传播趋势的关键阈值。通过构造合适的李雅普诺夫函数，严格证明当$R_0<1$ 时，无病平衡点是全局渐近稳定的；当$R_0>1$ 时，唯一的感染平衡点是全局渐近稳定的。数值模拟结果验证理论分析的正确性。参数敏感性分析亦揭示，宿主细胞的内在动力学是对$R_0$ 影响最大的因素。本研究为理解CHIKV的复杂感染动态及评估潜在干预策略提供有力的数学工具。

Abstract: To gain a deeper insight into the in-host infection mechanism of Chikungunya virus (CHIKV), we construct and analyze a four-dimensional dynamical model incorporating dual infection pathways. The model integrates two transmission routes, virus-to-cell and cell-to-cell, along with the Logistic growth of susceptible cells and B-cell mediated immune response. We derive the basic reproduction number, $R_0$ , and establish it as a key threshold for determining the trend of viral spread. By constructing suitable Lyapunov functions, we rigorously prove that the disease-free equilibrium is globally asymptotically stable when $R_0<1$ , and the unique endemic equilibrium is globally asymptotically stable when $R_0>1$ . Numerical simulations are performed, and the results validate our theoretical analysis. Furthermore, parameter sensitivity analysis reveals that the intrinsic dynamics of host cells have the most significant impact on $R_0$ . This study provides a robust mathematical tool for understanding the complex infection dynamics of CHIKV and for evaluating potential intervention strategies.