Designing a concert's stage and viewing platforms

to protect concert-goers from SARS-CoV-2

Refining government guidelines

for outdoor and indoor spaces.


To reduce the spread of COVID-19 by airborne (aerosol) transmission of SARS-CoV-2, it is necessary to identify the governing transport processes and parameters of air pollution.

The aim is to produce a theoretical model and predict spacial virus concentrations, as well as the growth rate of a contaminated region.

Given the approximate quanta emission rates of SARS-CoV-2, the viewing platforms and the stage are designed to accomodate a certain number of people.

The rates are different for people breathing at rest, breathing during heavy activity, speaking during light activity and speaking loudly/singing.

Outdoor Transmission of SARS-CoV-2

In the following simulation, 5 infected concert-goers are considered as distinct sources fixed in space. Using the analytical solution for advection-diffusion of a Gaussian plume, and at increasing times, two scenarios are considered: NO WIND and WIND. The standard advection-diffusion-reaction model deals with the time evolution of the virus in air. The mathematical equations describing this evolution are partial differential equations derived from mass balances. The overall change in concentration is described by the 2-D advection-diffusion equation:

\[ \frac{\partial}{\partial t} \left\langle\bar{C}(x,y,t) \right\rangle+\frac{\partial}{\partial x} \left(u(x,y)\left\langle\bar{C}(x,y,t) \right\rangle\right) + \frac{\partial}{\partial y}\left(v(x,y)\left\langle\bar{C}(x,y,t) \right\rangle \right) = \frac{\partial}{\partial x} \left(D_x \frac{\partial}{\partial x}\left\langle\bar{C}(x,y,t) \right\rangle\right) + \frac{\partial}{\partial y} \left(D_y \frac{\partial}{\partial y}\left\langle\bar{C}(x,y,t) \right\rangle\right) \]
\[x, y \in \mathbb{R} , t\geq0\]

The solution for the continuous release of COVID in two dimensions is given by: \[ C(x,y,t)= \frac{\dot{M}}{2\,\sqrt{{\pi}^2\,\sigma^2_x\,\sigma^2_y}}{e}^{-\frac{{\left(X-U_x\,t\right)}^2}{2\,\sigma^2_x}-\frac{{\left(Y-U_y\,t\right)}^2}{2\,\sigma^2_y}} \]