Dynamic behavior analysis of an $ SVIR $ epidemic model with two time delays associated with the COVID-19 booster vaccination time

Zimeng Lv; Xinyu Liu; Yuting Ding; Zimeng Lv; Xinyu Liu; Yuting Ding

doi:10.3934/mbe.2023261

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 6030-6061. doi: 10.3934/mbe.2023261

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Dynamic behavior analysis of an $ SVIR $ epidemic model with two time delays associated with the COVID-19 booster vaccination time

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Academic Editor: Xiang-Sheng Wang

Received: 16 November 2022 Revised: 15 January 2023 Accepted: 15 January 2023 Published: 18 January 2023

Since the outbreak of COVID-19, there has been widespread concern in the community, especially on the recent heated debate about when to get the booster vaccination. In order to explore the optimal time for receiving booster shots, here we construct an $ SVIR $ model with two time delays based on temporary immunity. Second, we theoretically analyze the existence and stability of equilibrium and further study the dynamic properties of Hopf bifurcation. Then, the statistical analysis is conducted to obtain two groups of parameters based on the official data, and numerical simulations are carried out to verify the theoretical analysis. As a result, we find that the equilibrium is locally asymptotically stable when the booster vaccination time is within the critical value. Moreover, the results of the simulations also exhibit globally stable properties, which might be more beneficial for controlling the outbreak. Finally, we propose the optimal time of booster vaccination and predict when the outbreak can be effectively controlled.
- COVID-19,
- booster vaccination,
- antibody failure,
- two time delays,
- Hopf bifurcation,
- normal form
Citation: Zimeng Lv, Xinyu Liu, Yuting Ding. Dynamic behavior analysis of an $ SVIR $ epidemic model with two time delays associated with the COVID-19 booster vaccination time[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6030-6061. doi: 10.3934/mbe.2023261

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Abstract

Since the outbreak of COVID-19, there has been widespread concern in the community, especially on the recent heated debate about when to get the booster vaccination. In order to explore the optimal time for receiving booster shots, here we construct an $ SVIR $ model with two time delays based on temporary immunity. Second, we theoretically analyze the existence and stability of equilibrium and further study the dynamic properties of Hopf bifurcation. Then, the statistical analysis is conducted to obtain two groups of parameters based on the official data, and numerical simulations are carried out to verify the theoretical analysis. As a result, we find that the equilibrium is locally asymptotically stable when the booster vaccination time is within the critical value. Moreover, the results of the simulations also exhibit globally stable properties, which might be more beneficial for controlling the outbreak. Finally, we propose the optimal time of booster vaccination and predict when the outbreak can be effectively controlled.

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