Open AccessMathematical modeling and stability analysis of the time-delayed $ SAIM $ model for COVID-19 vaccination and media coverage
Author(s) -
Xinyu Liu,
Zimeng Lv,
Yuting Ding
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022294
Subject(s) - hopf bifurcation , epidemic model , stability (learning theory) , vaccination , covid-19 , mass vaccination , econometrics , mathematics , media coverage , mathematical economics , statistics , computer science , bifurcation , demography , medicine , sociology , physics , virology , population , disease , pathology , quantum mechanics , nonlinear system , machine learning , infectious disease (medical specialty) , media studies
Since the COVID-19 outbreak began in early 2020, it has spread rapidly and threatened public health worldwide. Vaccination is an effective way to control the epidemic. In this paper, we model a $ SAIM $ equation. Our model involves vaccination and the time delay for people to change their willingness to be vaccinated, which is influenced by media coverage. Second, we theoretically analyze the existence and stability of the equilibria of our model. Then, we study the existence of Hopf bifurcation related to the two equilibria and obtain the normal form near the Hopf bifurcating critical point. Third, numerical simulations based two groups of values for model parameters are carried out to verify our theoretical analysis and assess features such as stable equilibria and periodic solutions. To ensure the appropriateness of model parameters, we conduct a mathematical analysis of official data. Next, we study the effect of the media influence rate and attenuation rate of media coverage on vaccination and epidemic control. The analysis results are consistent with real-world conditions. Finally, we present conclusions and suggestions related to the impact of media coverage on vaccination and epidemic control.