Transmission of airborne virus through sneezed and coughed droplets

The spread of COVID19 through droplets ejected by infected individuals during sneezing and coughing has been considered as a matter of key concern. Therefore, a quantitative understanding of the propagation of droplets containing virus assumes immense importance. Here we investigate the evolution of droplets in space and time under varying external conditions of temperature, humidity and wind flow by using laws of statistical and fluid mechanics. The effects of drag, diffusion and the gravity on droplets of different sizes and ejection velocities have been considered during their motion in the air. In still air we found that bigger droplets traverse larger distance but the smaller droplets remain suspended in the air for longer time. So, in still air the horizontal distance that a healthy individual should maintain from an infected one is determined by the bigger droplets but the time interval to be maintained is determined by the smaller droplets. We show that in places with wind flow the lighter droplets travel larger distance and remain suspended in the air for longer time. Therefore, we conclude that both temporal and the geometric distance that a healthy individual should maintain from an infected one is determined by the smaller droplets under flowing air which makes the use of mask mandatory to prevent the virus. The maintenance of only stationary separation between healthy and infected individuals is not substantiated. The quantitative results obtained here will be useful to devise strategies for preventing the spread of other types of droplets also containing microorganisms.