Dynamic Analysis of a COVID-19 Vaccination Model with a Positive Feedback Mechanism and Time-Delay

Xin Ai, Xinyu Liu, Yuting Ding and Han Li
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Xin Ai: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Xinyu Liu: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Yuting Ding: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Han Li: College of Economics and Management, Northeast Forestry University, Harbin 150040, China

Mathematics, 2022, vol. 10, issue 9, 1-24

Abstract: As the novel coronavirus pandemic has spread globally since 2019, most countries in the world are conducting vaccination campaigns. First, based on the traditional SIR infectious disease model, we introduce a positive feedback mechanism associated with the vaccination rate, and consider the time delay from antibody production to antibody disappearance after vaccination. We establish an U V a V model for COVID-19 vaccination with a positive feedback mechanism and time-delay. Next, we verify the existence of the equilibrium of the formulated model and analyze its stability. Then, we analyze the existence of the Hopf bifurcation, and use the multiple time scales method to derive the normal form of the Hopf bifurcation, further determining the direction of the Hopf bifurcation and the stability of the periodic solution of the bifurcation. Finally, we collect the parameter data of some countries and regions to determine the reasonable ranges of multiple parameters to ensure the authenticity of simulation results. Numerical simulations are carried out to verify the correctness of the theoretical results. We also give the critical time for controllable widespread antibody failure to provide a reference for strengthening vaccination time. Taking two groups of parameters as examples, the time of COVID-19 vaccine booster injection should be best controlled before 38.5 weeks and 35.3 weeks, respectively. In addition, study the impact of different expiration times on epidemic prevention and control effectiveness. We further explore the impact of changes in vaccination strategies on trends in epidemic prevention and control effectiveness. It could be concluded that, under the same epidemic vaccination strategy, the existence level of antibody is roughly the same, which is consistent with the reality.

Keywords: COVID-19 model; vaccination willingness; failure time of vaccine antibody; Hopf bifurcation; multiple time scales method; normal form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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