论文标题
疫苗接种的年龄结构性流行模型
An age-structured epidemic model with vaccination
论文作者
论文摘要
在本文中，我们通过疫苗接种构建了Covid-19的年龄结构化模型，并从多个角度进行分析。我们得出了独特的无病平衡点和基本的繁殖编号$ \ mathscr {r} _0 $，然后我们表明，当$ \ m atsscr {r} _0 <1 $时，无病的平衡在本地渐近稳定，而当$ \ nathscr时不稳定，则是不稳定的。我们还可以解决地方性平衡点并揭示稳定性。我们使用灵敏度分析来探讨参数如何影响$ \ mathscr {r} _0 $。灵敏度分析有助于我们制定更多针对性的控制流行病。最后，该模型用于讨论2021年初赫比省Shijiazhuang的案件。我们将报告的案例与模拟进行了比较，以评估Shijiazhuang政府采取的措施。我们的研究表明，年龄结构，疫苗接种和严重的遏制措施如何影响流行病。
In this article, we construct an age-structured model for COVID-19 with vaccination and analyze it from multiple perspectives. We derive the unique disease-free equilibrium point and the basic reproduction number $ \mathscr{R}_0 $, then we show that the disease-free equilibrium is locally asymptotically stable when $ \mathscr{R}_0 < 1 $, while is unstable when $ \mathscr{R}_0 > 1 $. We also work out endemic equilibrium points and reveal the stability. We use sensitivity analysis to explore how parameters influence $ \mathscr{R}_0 $. Sensitivity analysis helps us develop more targeted strategies to control epidemics. Finally, this model is used to discuss the cases in Shijiazhuang, Hebei Province at the beginning of 2021. We compare reported cases with the simulation to evaluate the measures taken by Shijiazhuang government. Our study shows how age structure, vaccination and drastic containment measures can affect the epidemic.
