Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA.
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada.
Math Biosci Eng. 2023 Jan 4;20(3):4816-4837. doi: 10.3934/mbe.2023223.
This paper is devoted to investigating the impact of vaccination on mitigating COVID-19 outbreaks. In this work, we propose a compartmental epidemic ordinary differential equation model, which extends the previous so-called SEIRD model by incorporating the birth and death of the population, disease-induced mortality and waning immunity, and adding a vaccinated compartment to account for vaccination. Firstly, we perform a mathematical analysis for this model in a special case where the disease transmission is homogeneous and vaccination program is periodic in time. In particular, we define the basic reproduction number $ \mathcal{R}_0 $ for this system and establish a threshold type of result on the global dynamics in terms of $ \mathcal{R}_0 $. Secondly, we fit our model into multiple COVID-19 waves in four locations including Hong Kong, Singapore, Japan, and South Korea and then forecast the trend of COVID-19 by the end of 2022. Finally, we study the effects of vaccination again the ongoing pandemic by numerically computing the basic reproduction number $ \mathcal{R}_0 $ under different vaccination programs. Our findings indicate that the fourth dose among the high-risk group is likely needed by the end of the year.
本文致力于研究接种疫苗对减轻 COVID-19 爆发的影响。在这项工作中，我们提出了一个房室传染病微分方程模型，通过纳入人口的出生和死亡、疾病导致的死亡和免疫力下降，以及增加一个接种疫苗的房室来解释接种疫苗的情况，对之前所谓的 SEIRD 模型进行了扩展。首先，我们在疾病传播是均匀的且接种计划在时间上是周期性的特殊情况下对该模型进行了数学分析。特别是，我们为这个系统定义了基本繁殖数$ \mathcal{R}_0 $，并根据$ \mathcal{R}_0 $建立了一个关于全局动力学的阈值类型的结果。其次，我们将我们的模型拟合到包括香港、新加坡、日本和韩国在内的四个地点的多个 COVID-19 波中，然后通过预测到 2022 年底 COVID-19 的趋势。最后，我们通过数值计算不同接种计划下的基本繁殖数$ \mathcal{R}_0 $，再次研究了接种疫苗对当前大流行的影响。我们的研究结果表明，到今年年底，高风险人群可能需要接种第四剂疫苗。
