Estimation of viral load and infection probability for a "mild" cough using direct numerical simulation

The transmission of virus-laden droplets from one person to another for COVID-19-type diseases is a fluid dynamical problem. Here we present results from direct numerical simulation of a "mild" cough flow using an Eulerian approximation for liquid droplets, which is valid for small droplet Stokes numbers. The Boussinesq-Navier-Stokes equations are solved numerically using a closure model for the droplet evaporation time scale. We estimate the viral exposure on an imaginary susceptible person by computing the liquid droplet flux through a circular region (approximating human face) at different distances from the infected speaker and using values of the number of virions per unit volume of cough liquid from the literature. We consider the inhalation of virions through the nose as well as exposure through the eyes and the mouth while determining the total viral load. The associated infection probability is then determined based on a characteristic infection dose. The resulting map of infection probability as a function of space and time can serve as an important input to epidemiological modelling. Moreover, the present scheme, being computationally inexpensive, can be used for determining long-range transmission of infectious droplets and the resulting spread of airborne diseases.