Effects of vaccination on mitigating COVID-19 outbreaks: a conceptual modeling approach

Allison Fisher; Hainan Xu; Daihai He; Xueying Wang; Allison Fisher; Hainan Xu; Daihai He; Xueying Wang

doi:10.3934/mbe.2023223

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4816-4837. doi: 10.3934/mbe.2023223

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Effects of vaccination on mitigating COVID-19 outbreaks: a conceptual modeling approach

1.
Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
2.
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada
3.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

Received: 25 June 2022 Revised: 25 October 2022 Accepted: 30 October 2022 Published: 04 January 2023

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 ^[1,2,3,4] 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.
- COVID-19,
- vaccination,
- SEIRD model,
- reproduction number,
- threshold dynamics
Citation: Allison Fisher, Hainan Xu, Daihai He, Xueying Wang. Effects of vaccination on mitigating COVID-19 outbreaks: a conceptual modeling approach[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4816-4837. doi: 10.3934/mbe.2023223

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Abstract

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 ^[1,2,3,4] 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.

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