Department of Mathematics, Northeast Forestry University, Harbin 150040, China.
Math Biosci Eng. 2022 Apr 19;19(6):6296-6316. doi: 10.3934/mbe.2022294.
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.
自 2020 年初 COVID-19 爆发以来，它迅速传播，威胁着全球公共卫生。接种疫苗是控制疫情的有效方法。在本文中，我们建立了一个 SAIM 方程模型。我们的模型涉及接种疫苗和人们改变接种意愿的时间延迟，这受到媒体报道的影响。其次，我们从理论上分析了模型平衡点的存在性和稳定性。然后，我们研究了与两个平衡点相关的 Hopf 分岔的存在性，并在 Hopf 分岔临界点附近得到了正规型。第三，我们基于两组模型参数进行了数值模拟，以验证我们的理论分析，并评估稳定平衡点和周期解等特征。为了确保模型参数的适当性，我们对官方数据进行了数学分析。接下来，我们研究了媒体影响率和媒体报道衰减率对疫苗接种和疫情控制的影响。分析结果与实际情况一致。最后，我们提出了与媒体报道对疫苗接种和疫情控制的影响相关的结论和建议。
