One of the many unresolved questions that revolves around the Covid-19 pandemic is whether local outbreaks can depend on ambient conditions like temperature and relative humidity. In this paper, we develop a model that tries to explain and describe the temperature and relative humidity sensitivity of respiratory droplets and their possible connection in determining viral outbreaks. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism - the final equations of which are similar to the well-known SIR model. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time accounting for droplet cooling, heat and mass transfer and finally crystallization of the salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. Droplet evaporation/desiccation time is indeed dependent on ambient temperature and relative humidity, considered at both outdoor and indoor conditions. Since the droplet evaporation time determines the infection rate constant, ambient temperature and relative humidity are shown to impact the outbreak growth rates.

中文翻译：

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模拟呼吸道飞沫在 Covid-19 型大流行中的作用

围绕 Covid-19 大流行的众多悬而未决的问题之一是，局部爆发是否取决于温度和相对湿度等环境条件。在本文中，我们开发了一个模型，试图解释和描述呼吸道飞沫的温度和相对湿度敏感性及其在确定病毒爆发方面的可能联系。该模型有两个部分。首先，我们基于反应机制对感染人口的增长率进行建模——其最终方程类似于众所周知的 SIR 模型。使用反应机制对大流行进行建模的优点是速率常数具有合理的物理解释。感染率常数是使用碰撞率理论推导出来的，它是呼吸道飞沫寿命的函数。在第二部分，我们将导致疾病传播的呼吸道飞沫模拟为盐溶液飞沫，并计算了它们的蒸发时间，其中考虑了飞沫冷却、热量和质量传递以及最终盐的结晶。模型输出分别与实验获得的纯水和盐溶液悬浮液滴的蒸发特性进行了比较，确保了模型的保真度。在室外和室内条件下，液滴蒸发/干燥时间确实取决于环境温度和相对湿度。由于液滴蒸发时间决定了感染率常数，因此环境温度和相对湿度会影响爆发增长率。