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One of the many unresolved questions that revolves around the Covid-19pandemic is whether local outbreaks can depend on ambient conditions liketemperature and relative humidity. In this paper, we develop a model that triesto explain and describe the temperature and relative humidity sensitivity ofrespiratory droplets and their possible connection in determining viraloutbreaks. The model has two parts. First, we model the growth rate of theinfected population based on a reaction mechanism - the final equations ofwhich are similar to the well-known SIR model. The advantage of modeling thepandemic using the reaction mechanism is that the rate constants have soundphysical interpretation. The infection rate constant is derived using collisionrate theory and shown to be a function of the respiratory droplet lifetime. Inthe second part, we have emulated the respiratory droplets responsible fordisease transmission as salt solution droplets and computed their evaporationtime accounting for droplet cooling, heat and mass transfer and finallycrystallization of the salt. The model output favourably compares with theexperimentally obtained evaporation characteristics of levitated droplets ofpure water and salt solution, respectively, ensuring fidelity of the model.Droplet evaporation/desiccation time is indeed dependent on ambient temperatureand relative humidity, considered at both outdoor and indoor conditions. Sincethe droplet evaporation time determines the infection rate constant, ambienttemperature and relative humidity are shown to impact the outbreak growthrates.

Modeling ambient temperature and relative humidity sensitivity of respiratory droplets and their role in Covid-19 outbreaks