Numerical and theoretical modeling for transmission of droplet carrying virus

Safe social distance is an important parameter for the prevention and treatment of a virus transmitted through droplets. However, the distance selected is not suitable for all air environments, and the calculation method of fluid research is time-consuming. Therefore, rapid and accurate prediction of safe social distance is the key to epidemic prevention and control. However, it is difficult for the existing fluid research to obtain the safe social distance rapidly. In this study, we set up a simple and effective numerical model and develop codes that combine the effects of evaporation, drag force, and gravity. We further conducted numerical simulations to investigate the motion of droplets in various air conditions. We completed a single case simulation with only one core and within several minutes, and determined that the resistance time and velocity evolution directly impact the transmission distance. We also observed two-stage regularity of motions in both the vertical and horizontal directions, and competition between evaporation and vertical falling. In addition, we derived a set of analytical solutions to describe the evaporation time and vertical and horizontal distances. The results demonstrated the good accuracy of the predicted data. Herein, we obtained an approximate rather than an accurate solution and, together with empirical coefficients, fitted it based on our numerical simulation. The proposed method can provide a rapid and accurate estimation of safe social distances for various environmental conditions. Common clinical cases were also analyzed, and prevention and control recommendations were provided based on the outcomes of the study.