Stochastic Transmission of Sneezed and Coughed Droplets -- Physicists' Perspective

Das, Santosh K.; Alam, Jan-e; Plumari, Salvatore; Greco, Vincenzo

The motion of droplets ejected in the air during sneezing, coughing, breathing and speaking has been studied within the scope of Langevin stochastic differential equation. The effects of drag, diffusion and the gravity on the droplets during its motion in the air have been taken into account. We found that the distance traveled by a droplet released at an average human height by an infected individual strongly depends on the velocity of ejection and mass of the droplet. For example, a droplet of radius 100 $\mu$m and mass 4186 nano-gm released at a height of 1.7 meter will travel 2.35 meter distance horizontally before settling gravitationally. The same droplet with lower ejection velocity of 5 m/s will travel a horizontal distance of 0.55 meter approximately. We found that the gravitational force does not allow larger (and hence massive) droplets to remain suspended in the air for long. Because the gravitational force is superior to the the drag force exerted by the air molecules on larger droplets. However, for smaller droplets the drag force dominates over the gravitational force which allows it to be suspended in the air for longer time. As an instance a droplet of radius 2.5 $\mu$m may remain suspended in the air for more than half an hour. This suggests that a healthy individual should maintain temporal distance from an infected one to avoid virus suspended in the air. Therefore, as preventive strategies a healthy individual should not only maintain geometric distance from an infected one but also temporal distance to deter the floating smaller droplets by covering nose, mouth, etc. This approach will be useful for the prevention of current COVID19 pandemic.