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The use of mathematical analysis in understanding epidemics is essential in predicting the progression of diseases over time and in providing direction to decision-makers with respect to public health policy. It is within this context that the purpose of this work is to study a stochastic model of COVID-19 disease dynamics. In our SIR mathematical model, the transmission of the infection from infected individuals to susceptible individuals occurs at a rate \(\beta \) , which is disrupted by white noise. Our work starts with the investigation of the well-posedness of the mathematical model. Then, we present the sufficient conditions for the COVID-19 extinction and persistence in mean of this pandemic. It moves then to the investigation of certain numerical findings to support the theoretical analysis and to show the effectiveness of quarantine strategy in controlling the COVID-19 pandemic. The theoretical findings and the numerical results align well. Finally, we show numerically the effectiveness of quarantine strategy in controlling the spread of COVID-19 infection. Controlling the infection severity may help to achieve some of sustainable development goals.

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A Mathematical Model for the Impacts of Vaccination and Quarantine on the Dynamics of COVID-19 Pandemic: Deterministic and Stochastic Analysis

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  • 发表日期：

    2025年

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  • Marya Sadki,
  • Karam Allali

摘要

The use of mathematical analysis in understanding epidemics is essential in predicting the progression of diseases over time and in providing direction to decision-makers with respect to public health policy. It is within this context that the purpose of this work is to study a stochastic model of COVID-19 disease dynamics. In our SIR mathematical model, the transmission of the infection from infected individuals to susceptible individuals occurs at a rate \(\beta \) , which is disrupted by white noise. Our work starts with the investigation of the well-posedness of the mathematical model. Then, we present the sufficient conditions for the COVID-19 extinction and persistence in mean of this pandemic. It moves then to the investigation of certain numerical findings to support the theoretical analysis and to show the effectiveness of quarantine strategy in controlling the COVID-19 pandemic. The theoretical findings and the numerical results align well. Finally, we show numerically the effectiveness of quarantine strategy in controlling the spread of COVID-19 infection. Controlling the infection severity may help to achieve some of sustainable development goals.