Moussaoui Ali, Zerga El Hadi
Laboratoire d'Analyse Non linéaire et Mathématiques Appliquées, Department of Mathematics, University of Tlemcen, Algeria.
AIMS Public Health. 2020 Oct 30;7(4):816-827. doi: 10.3934/publichealth.2020063. eCollection 2020.
We propose an SIR epidemic model taking into account prevention measures against coronavirus disease 2019 (COVID-19) such as wearing masks and respecting safety distances. We look for the conditions to avoid a second epidemic peak in the phase of release from confinement. We derive equations for the critical levels of mask efficiency, mask adoption (fraction of population wearing masks) and fraction of population engaging in physical distancing that lower the basic reproduction number to unity. Conclusions: For = 2.5, if at least 40% of people wear masks with efficiency 50%, and at least 20% of the population without masks (or anti-maskers) respect physical distancing measures, the effective reproduction number can be reduced to less than 1 and COVID-19 infections would plummet. The model predicts also that if at least half of the people respecting physical distancing, COVID-19 outbreaks with of about 3, would be theoretically extinguished without wearing masks. The results of this study provide an alternative explanation for the spread of the disease, and suggest some valuable policy recommendations about the control strategies applied to mitigate disease transmission.
我们提出了一种考虑针对2019冠状病毒病(COVID-19)预防措施(如佩戴口罩和保持安全距离)的SIR传染病模型。我们探寻在解除封锁阶段避免出现第二轮疫情高峰的条件。我们推导了口罩效率、口罩佩戴率(佩戴口罩的人口比例)以及采取物理距离措施的人口比例的临界水平方程,这些临界水平可将基本再生数降至1。结论:对于R0 = 2.5,如果至少40%的人佩戴效率为50%的口罩,且至少20%不戴口罩的人(或反对戴口罩者)遵守物理距离措施,则有效再生数可降至1以下,COVID-19感染人数将大幅下降。该模型还预测,如果至少一半的人遵守物理距离措施,理论上R0约为3的COVID-19疫情将在不佩戴口罩的情况下得到控制。本研究结果为疾病传播提供了另一种解释,并就减轻疾病传播的控制策略提出了一些有价值的政策建议。