Atangana Ernestine, Atangana Abdon
Centre for Environmental Management, Faculty of Natural and Agricultural Science, University of the Free State Bloemfontein, 9301, South Africa.
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9301 Bloemfontein, South Africa.
Results Phys. 2020 Dec;19:103425. doi: 10.1016/j.rinp.2020.103425. Epub 2020 Sep 30.
In the last few months, the spread of COVID-19 among humans has caused serious damages around the globe letting many countries economically unstable. Results obtained from conducted research by epidemiologists and virologists showed that, COVID-19 is mainly spread from symptomatic individuals to others who are in close contact via respiratory droplets, mouth and nose, which are the primary mode of transmission. World health organization regulations to help stop the spread of this deadly virus, indicated that, it is compulsory to utilize respiratory protective devices such as facemasks in the public. Indeed, the use of these facemasks around the globe has helped reduce the spread of COVID-19. The primary aim of facemasks, is to avoid inhaling air that could contain droplets with COVID-19. We should note that, respiration process is the movement of oxygen from external atmosphere to the cells within tissue and the transport of carbon dioxide outside. However, the rebreathing of carbon dioxide using a facemask has not been taken into consideration. The hypercapnia (excess inhaled content of CO) has been recognized to be related to symptoms of fatigue, discomfort, muscular weakness, headaches as well as drowsiness. Rebreathing of CO has been a key to concern regarding the use of a facemask. Rebreathing usually occur when an expired air that is rich in CO stays long than normal in the breathing space of the respirator after a breath. The increase of the arterial CO concentration leads to symptoms that are aforementioned. Studies have been conducted on facemask shortages and on the appropriate facemask required to reduce the spread of COVID-19; however no study has been conducted to assess the possible relationship between CO inhalation due to facemask, to determine and recommend which mask is appropriate in the reduction of the spread of the coronavirus while simultaneously avoid CO inhalation by the facemask users. In the current paper, we provided a literature review on the use of facemasks with the aim to determine which facemasks could be used to avoid re-inhaling rejected CO. Additionally, we presented mathematical models depicting the transport of COVID-19 spread through wind with high speed. We considered first mathematical models for which the effect air-heterogeneity is neglected, such that air flow follows Markovian process with a retardation factor, these models considered two different scenarios, the speed of wind is constant and time-space dependent. Secondly, we assumed that the wind movement could follow different processes, including the power law process, fading memory process and a two-stage processes, these lead us to use differential operators with power law, exponential decay and the generalized Mittag-Leffler function with the aim to capture these processes. A numerical technique based on the Lagrange polynomial interpolation was used to solve some of these models numerically. The numerical solutions were coded in MATLAB software for simulations. The results obtained from the mathematical simulation showed that a wind with speed of 100 km/h could transport droplets as far as 300 m. The results obtained from these simulations together with those presented by other researchers lead us to conclude that, the wind could have helped spread COVID-19 in some places around the world, especially in coastal areas. Therefore, appropriate facemasks that could help avoid re-inhaling enough CO should be used every time one is in open air even when alone especially in windy environment.
在过去几个月里,新冠病毒在人类中的传播给全球造成了严重破坏,许多国家的经济因此不稳定。流行病学家和病毒学家进行的研究结果表明,新冠病毒主要通过呼吸道飞沫,从有症状的个体传播给密切接触的其他人,口鼻是主要传播途径。世界卫生组织制定了相关规定以帮助阻止这种致命病毒的传播,规定在公共场所必须使用口罩等呼吸道防护设备。事实上,全球范围内使用这些口罩有助于减少新冠病毒的传播。口罩的主要目的是避免吸入可能含有新冠病毒飞沫的空气。我们应该注意到,呼吸过程是氧气从外部大气进入组织内细胞以及二氧化碳排出体外的过程。然而,使用口罩时二氧化碳的再吸入问题尚未得到考虑。高碳酸血症(吸入过多的二氧化碳)已被认为与疲劳、不适、肌肉无力、头痛以及嗜睡等症状有关。二氧化碳的再吸入一直是使用口罩的一个关键问题。再吸入通常发生在呼出的富含二氧化碳的空气在呼吸后在呼吸器的呼吸空间中停留时间比正常情况长的时候。动脉血二氧化碳浓度的升高会导致上述症状。已经有关于口罩短缺以及减少新冠病毒传播所需合适口罩的研究;然而,尚未有研究评估因使用口罩导致的二氧化碳吸入之间可能的关系,以确定并推荐哪种口罩在减少冠状病毒传播的同时能避免口罩使用者吸入二氧化碳。在本文中,我们提供了一篇关于口罩使用的文献综述,旨在确定哪些口罩可用于避免再次吸入呼出的二氧化碳。此外,我们还展示了描述新冠病毒通过高速风传播的数学模型。我们首先考虑了忽略空气非均匀性影响的数学模型,使得气流遵循具有延迟因子的马尔可夫过程,这些模型考虑了两种不同情况,风速恒定和时空相关。其次,我们假设风的运动可以遵循不同的过程,包括幂律过程、衰退记忆过程和两阶段过程,这使我们使用具有幂律、指数衰减和广义米塔格 - 莱夫勒函数的微分算子来捕捉这些过程。基于拉格朗日多项式插值的数值技术被用于对其中一些模型进行数值求解。数值解在MATLAB软件中编码进行模拟。数学模拟得到的结果表明,风速为100公里/小时的风可以将飞沫传播至300米远。这些模拟结果以及其他研究人员的结果使我们得出结论,风可能在世界上一些地方,特别是沿海地区,助力了新冠病毒的传播。因此,即使独自一人处于户外,尤其是在有风的环境中时,每次都应使用能够帮助避免再次吸入足够二氧化碳的合适口罩。