具有疫苗接种的COVID-19传播模型的动力学分析

Dynamical Analysis of a COVID-19 Transmission Model with Vaccination

摘要: 自COVID-19出现以来，毒株不断变异，毒性变小、传播性增强，多数专家认为我们将与COVID-19长期共存。由于是否出现重症患者很大程度取决于个体免疫力，因此处于高危人群的老人和儿童长期面临威胁。此外由于没有治疗COVID-19的特效药物，加之多次感染新冠会对人体带来诸多后遗症，因此许多国家都在研发和接种针对最新变异毒株可以有效减少患重症和死亡的新型疫苗。并且由于毒株变异和免疫逃逸，我们将持续研发有效且快速生效的新型疫苗。因此本文提出了一个具有疫苗接种时滞的SVIAR传染病模型，计算了模型的控制再生数，研究了模型的动力学特征。文末的数值模拟验证了理论结果，并且分析了疫苗接种率和疫苗生效时间对疫情防控的影响，给出了对应的疫苗接种策略。

Abstract: Since the emergence of COVID-19, the viral strains have continuously mutated, with reduced virulence and enhanced transmissibility. Most experts believe that we will coexist with COVID-19 in the long term. As the severity of infection largely depends on individual immunity, older adults and children in high-risk groups face prolonged threats. Additionally, due to the lack of specific drugs for treating COVID-19, and considering that multiple infections with the novel coronavirus can lead to various lingering effects, many countries are developing and administering novel vaccines targeting the latest mutant strains to effectively reduce severe cases and fatalities. Furthermore, due to ongoing viral mutations and immune evasion, we will continue to research and develop efficient and rapidly effective new vaccines. Therefore, this article proposes an SVIAR infectious disease model with vaccination delays, calculates the model’s basic reproduction number, investigates its dynamic characteristics, and validates theoretical results through numerical simulations. The analysis also explores the impact of vaccination rates and vaccine efficacy duration on epidemic control, providing corresponding vaccination strategies.