A fractional stochastic model for aerosol transmission of fluid droplets and virus exposure in closed spaces

Abstract

Considering fractional Brownian motion $B^H_t$ and fractional white noise $W^H_t$ as a generalized stochastic processes in the framework of white noise analysis, we use them to model aerosol transmission of fluid droplets and virus exposure in closed space. The model is based on an airflow produced during coughing or sneezing governed by the incompressible Navier-Stokes equation, leading to the expulsion of contaminated aerosols that diffuse in a closed room and are subjected to random movements due to collision with other particles in the air. The proposed model involves stochastic components to grasp the uncertain nature of the aerosol diffusion and fractional derivatives to grasp the possibilities of a sub-diffusion or super-diffusion effect due to various physical conditions in the room. We prove existence and uniqueness of the solution to the proposed model, supported by numerical simulations and experiments.