Mathematical Modelling of Dynamic Behavior of Droplets of Saliva as a Vehicles for Respiratory Pathogens Transmission

This study performs an analytical description of the dynamic behavior of the droplets and the effect of the environmental air temperature on their drop time and horizontal velocity to highlight some aspects that improve the fight against the spread of the respiratory pathogens, such as the COVID-19, between humans. According to this study, when the droplet exits the human body, its horizontal velocity reduces drastically. The smaller the size of the droplets, the higher is the rate of this decay. The droplets achieve its largest horizontal range instantaneously. Thus, the horizontal displacement for droplets with less than 100 µm in diameter does not exceed 380 mm. However, droplets with larger than 300 µm in diameter have a horizontal range that can reach distances greater than 1600 mm, without significant reduction of their heights to the ground. This can invalid the current rule of social distance (least 1.5 m — 2 m between people). Because of this, if a person is within the horizontal displacement range of a droplet he will be hit in the face which can increase the contagion. The droplets with less than 1 µm in diameter remain airborne for at least 15 hours, which can further increase of contagion by inhalation. The temperature of the environment has a negative influence on droplets drop time. Faced with this, the people in warmer countries can inhale more virus of suspension than those in colder countries. Finally, the higher the environmental air temperature, the lower the horizontal range achieved by the droplets.