Modeling and global stability analysis of COVID-19 dynamics with optimal control and cost-effectiveness analysis

Q1 Mathematics Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-01 Epub Date: 2024-07-26 DOI:10.1016/j.padiff.2024.100843

Hailay Weldegiorgis Berhe , Abadi Abay Gebremeskel , Zinabu Teka Melese , Mo’tassem Al-arydah , Asdenaki Aklilu Gebremichael

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Abstract

In addressing the global challenges posed by COVID-19, this study introduces a mathematical model aimed at investigating the transmission dynamics of COVID-19 and forwarding strategies for controlling it. By employing Lyapunov functions, we perform a thorough stability analysis of both disease-free and endemic equilibria. We calibrated the model using daily COVID-19 data from early 2022 in Ethiopia, after vaccination initiation. A global sensitivity analysis confirmed the robustness of the model. In addition, we extended the model to address optimal control by incorporating vaccination, public health education, and treatment. Our findings highlight the effectiveness of individual control measures and reveal that vaccination, public health educational campaign and treatment is the most cost-effective method for mitigating COVID-19 spread.

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利用优化控制和成本效益分析对 COVID-19 动态进行建模和全局稳定性分析

为应对 COVID-19 带来的全球性挑战，本研究引入了一个数学模型，旨在研究 COVID-19 的传播动态以及控制 COVID-19 的转发策略。通过使用 Lyapunov 函数，我们对无疾病和地方病均衡状态进行了全面的稳定性分析。我们使用埃塞俄比亚 2022 年初开始接种疫苗后的 COVID-19 每日数据对模型进行了校准。全局敏感性分析证实了模型的稳健性。此外，我们还对模型进行了扩展，通过纳入疫苗接种、公共卫生教育和治疗来解决最优控制问题。我们的研究结果凸显了单项控制措施的有效性，并揭示了疫苗接种、公共卫生教育活动和治疗是减缓 COVID-19 传播的最具成本效益的方法。

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