Hayden Matthew, Morrow Bryce, Yang Wesley, Wang Jin
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA.
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA.
Math Biosci Eng. 2023 Jan;20(1):587-612. doi: 10.3934/mbe.2023027. Epub 2022 Oct 12.
There is an ongoing debate on the different transmission modes of SARS-CoV-2 and their relative contributions to the pandemic. In this paper, we employ a simple mathematical model, which incorporates both the human-to-human and environment-to-human transmission routes, to study the transmission dynamics of COVID-19. We focus our attention on the role of airborne transmission in the spread of the disease in a university campus setting. We conduct both mathematical analysis and numerical simulation, and incorporate published experimental data for the viral concentration in the air to fit model parameters. Meanwhile, we compare the outcome to that of the standard SIR model, utilizing a perturbation analysis in the presence of multiple time scales. Our data fitting and numerical simulation results show that the risk of airborne transmission for SARS-CoV-2 strongly depends on how long the virus can remain viable in the air. If the time for this viability is short, the airborne transmission route would be inconsequential in shaping the overall transmission risk and the total infection size. On the other hand, if the infectious virus can persist in aerosols beyond a few hours, then airborne transmission could play a much more significant role in the spread of COVID-19.
关于严重急性呼吸综合征冠状病毒2（SARS-CoV-2）的不同传播模式及其对疫情的相对贡献，目前存在着持续的争论。在本文中，我们采用一个简单的数学模型，该模型纳入了人际传播和环境-人传播途径，以研究新型冠状病毒肺炎（COVID-19）的传播动态。我们将注意力集中在空气传播在大学校园环境中疾病传播中的作用。我们进行了数学分析和数值模拟，并纳入已发表的空气中病毒浓度实验数据来拟合模型参数。同时，我们利用多时间尺度下的摄动分析，将结果与标准的易感-感染-康复（SIR）模型的结果进行比较。我们的数据拟合和数值模拟结果表明，SARS-CoV-2空气传播的风险很大程度上取决于病毒在空气中能够保持存活的时间。如果这种存活时间很短，那么空气传播途径在形成总体传播风险和总感染规模方面将无关紧要。另一方面，如果传染性病毒能够在气溶胶中持续数小时以上，那么空气传播在COVID-19的传播中可能会发挥更为重要的作用。
