一类SVEAIR周期传染病模型的动力学分析

Dynamic Analysis of a SVEAIR Periodic Infectious Disease Model

摘要: 本研究构建了一类周期环境下具有疫苗接种和无症状感染的SVEAIR型传染病模型。通过计算模型的基本再生数，我们建立了用于判定疾病是否流行的阈值理论。为了深入了解模型的全局动力学行为，我们借助于阈值理论给出了疾病灭绝性和一致持久性条件。证明了当基本再生数R₀ < 1时，模型的无病平衡点是全局渐近稳定的；当基本再生数R₀ > 1时，模型存在唯一的正周期解且疾病持续存在。最后通过数值模拟验证了模型的主要结果，这一研究为理解和控制此类周期传染病的传播提供了重要的理论基础。

Abstract: This study proposes a SVEAIR-type infectious disease model in a periodic environment, incorpo-rating both vaccine coverage and asymptomatic infections. By calculating the model’s basic re-production number, we establish a threshold theory to determine whether the disease becomes endemic. To gain a deeper understanding of the global dynamics of the model, we utilize the threshold theory to provide conditions for disease extinction and persistence. It is demonstrated that when the basic reproduction number is less than 1, the disease-free equilibrium point of the model is globally asymptotically stable; when the basic reproduction number is greater than 1, the model exhibits a unique positive periodic solution, indicating the persistence of the disease. Finally, the main results of the model are verified by numerical simulation, which provides an important theoretical basis for understanding and controlling the spread of such periodic infectious diseases.