诺如病毒传播的动力学建模与稳定性分析
Dynamic Modeling and Stability Analysis of Norovirus Transmission
摘要: 本文针对诺如病毒在“人类–贝类–家畜–水源”间的多宿主循环传播特性，构建了多宿主传染病动力学模型，刻画了诺如病毒随时间的演化规律。通过计算基本再生数 R 0 ，给出了阈值定理。借助单调动力系统和极限系统理论，证明了当 R 0 <1 时，无病平衡点的全局渐近稳定，病毒可逐步消亡；当 R 0 >1 时，系统存在唯一全局稳定的地方病平衡点，病毒持续流行。数据拟合和数值模拟结果进一步验证了模型和所得结论的合理性，为实现诺如病毒的精准防控提供理论支持。
Abstract: In view of the multi-host cyclic transmission of norovirus among humans, shellfish, livestock, and water sources, this paper constructs a dynamical model to characterize the temporal evolution of the virus. By calculating the basic reproduction number, we establish the threshold theorem. Utilizing the theory of monotone dynamical systems and limit systems, we prove that when the basic reproduction number is below unity, the disease-free equilibrium is globally asymptotically stable, indicating that the virus will eventually die out; when it exceeds unity, the system admits a unique globally stable endemic equilibrium, implying that the virus will persist endemically. Numerical simulations and data fitting confirm the model’s validity, laying a theoretical foundation for precision prevention and control strategies against norovirus.
文章引用：陈莉湘, 吕贵臣. 诺如病毒传播的动力学建模与稳定性分析[J]. 理论数学, 2026, 16(9): 62-76. https://doi.org/10.12677/pm.2026.169199

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