# COVID-19 Particle Collider $^{-\,\,part\,\,{1} / {3}\,\,-}$

INRAe\Olivier Vitrac - last update $2020-05-07$

Jump to Part 2, Part 3. The project has been forked here.

DISCLAIMER. COVID-19 Particle Collider is an experimental project showing how the propagation of COVID-19 virus can be described as a diffusion-controlled bimolecular chemical reaction (to be infected, you need to meet a contagious/"active" intermediate-product) and subsequent monomolecular ones.

The source and output files are freely available. Results and analyses are presented "AS IS".

## Content

$2020-04-14$ First on-line release ($webm$ and $h265$ movies). $2020-04-17$ Generalization to arbitrary geometries, revised DISCLAIMER. $2020-04-20$ Add link to Part 2 and justifications for large balls representing walls in the last section (same collision code used in Parts 1 and 2). $2020-05-07$ Add link to Part 3

## Short description

The propagation of viruses between individuals is very similar to diffusion-limited reactions. Based on this analogy, COVID-19 Particle Collider has been developed assuming that individuals are heavy spherical particles (with finite size) moving on and colliding with each others on a closed 2D domain. The domain itself is finite and without periodic boundary condition. The system is simulated out of equilibrium starting usually from a single infected particle (individual). Particles are either fixed (confined individuals) or free to move (non-confined individuals). Trajectories are ballistic from an initial prescribed distribution. The contamination chain propagates as Markov process involving four states: covid sensitive (confined or not), infected, recovered, and sick. The evolution of the infected individual is stochastic and governed by exponential distributions triggered from the first infection time.

The computer code provides more details on hypotheses and can be parameterized for various shapes (offices, city, country), various number of individuals, particle densities, rates of confinement and exposed surfaces. Current simulations assume a circular domain and depict a period of 30 days. The collisions are elastic and total momentum is preserved (microcanonical ensemble). Small particles move consequently much faster than large ones. Due to the multiple collisions, the displacements are rapidly random between particles. Traveled distances depends on particle densities, their size and time.

## Realistic simulations with two populations

The presented simulations comprise 80 confined (wall) particles and 195 non-confined (free) particles. They have all the same size. Since the evolutions are entirely stochastic, the conclusions can be inferred from only stable structures observed between different repetitions.

## Effects of concentration

Part 3 is devoted to density/concentration effects.

## Changing the mobility of particles/individuals

Changing the size (and therefore the weight) of particles introduce strong heterogeneities in the speeds of particles and in traveled distances. Small particles became tFirst on-line release ($webm$ and $h265$ movies)he main vector of the infection, they can reach both confined and non-confined ones. The differences between confined and non-confined became much lower.

### Simulation #1 (patient 0 with small size)

The initially infected particle is small (see 1-2 pm.) and therefore fast.

### Simulation #2 (patient 0 with small size)

The initially infected particle is small (see 11 am.) and therefore fast.

### Simulation #3 (patient 0 with intermediate size)

The initially infected particle is intermediate (see 5 pm.) and therefore fast.

## How fast infection can start/restart in closed systems

Home containment has been proposed to contain the pandemic. Without isolation of the $Covid\ominus$ and $Covid\oplus$ populations, the outbreak may restart rapidly. Previous simulations have been modified to describe an area representing business premises or buildings. The gray balls here represent the walls. The time scale is accelerated.

One single contagious person/particle (orange) is initially in the central room. As in previous simulations, transmission occurs immediately (without delay) when one $Covid\ominus$ particle collides/contacts a $Covid \oplus$ . The new $Covid \oplus$ becomes instantaneously contagious. All trajectories are ballistic with random reflections on walls. The shapes of "rooms" enable larger mean-free-paths and make the trajectories look more realistic for humans.

Please note that the described conditions exaggerate dramatically the risk of transmission.

The simulation below describes only one configuration, several configurations are shown in part 2.

NOTE: The upper sub-particle (confined) remains static because there are no more confined particles/individuals. Representing walls are as large balls, on which the moving particles bounce, enable to reuse the same code for different purposes and more complex geometries. In Part 2, the linkage between the different simulations is not preserved and the plots are reorganized.

Olivier (day 66 after the outbreak, as counted by COVID19 Forecast) - Based on these similations, it is obvious that you have to keep your social distance. For any question, send an email to the author.