中文标题：COVID-19流行病模型的全局稳定性与最优控制

作者：Fengsheng Chien, Hassan Saberi Nik, Mohammad Shirazian and J. F. Gómez-Aguilar

期刊：INTERNATIONAL JOURNAL OF BIOMATHEMATICS，国际生物数学杂志；中科院2区

DOI：https://doi.org/10.1142/S179352452350002X

ABSTRACT：This paper considers stability analysis of a Susceptible-Exposed-Infected-RecoveredVirus (SEIRV) model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission. The Lyapunov function using Volterra–Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium point. An optimal control strategy is proposed to prevent the spread of coronavirus, in addition to governmental intervention. The objective is to minimize together with the quantity of infected and exposed individuals while minimizing the total costs of treatment. A numerical study of the model is also carried out to investigate the analytical results.

摘要：本文对具有非线性发病率的SEIRV（易感-暴露-感染-康复-病毒）模型进行稳定性分析，旨在揭示疾病传播控制因素的有效性与局限性。通过采用基于Volterra Lyapunov矩阵的Lyapunov函数方法，实现了对地方病平衡点全局稳定性的研究。在政府干预措施之外，本文进一步提出预防冠状病毒传播的最优控制策略，该策略在最小化感染者和暴露者数量的同时，还能有效降低治疗总成本。通过数值模拟对理论分析结果进行了验证。