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

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

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Go back to Part 1, Part 2. 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

Updates

$2020-05-07$ First on-line release of Part 3 (be sure to have read part 1 before).

 

The effect of concentration or particle density

At a time when several countries are discussing the possibilities of reducing or even eliminating containment, let us look at the concentration effects, which in fact reflect the distance that must be traveled before encountering another particle. If the distance between contacts is greater, an "infected" (orange) particle is more likely to evolve spontaneously to a "recovered" (green) state before coming into contact with a "susceptible" particle.

Hypotheses

As in part 1, the particles that make up the walls of the domain are frozen/confined particles (immobile but which can be infected). The particle density is modified by keeping the same number of free particles (195) and increasing the surface area of the disk and thus its radius. The size of the particles is unchanged but they will appear smaller. Because there are fewer "collisions" when the density is lower (greater distances to cross), the animations are accelerated to visually maintain a similar number of collisions. The physical time is unchanged with a duration of 30 days. Note that there are more confined particles as the density is reduced.

The kinetics of the number of infected particles (orange curve) reflect the so-called distancing effects. This is not a video game and the animations do not look "impressive". As discussed in part 1, and part 2, a ballistic trajectory of each particle describes some displacements in a environment without or with obstacles. Obstacles are required only to describe the details of interactions in buildings, but unnecessary to describe "social" interactions at coarser scale. From a physical point of view, the presented simulations describe displacements in phase space as ballistic trajectories. The evolution is governed by the distribution of the pair correlation function between particles, that is the probability meet a particle within a distance $r$. The reproduction rate decrease as $\langle r\rangle^{-1}$ (reciprocal average distance between particles ) since all particles translate at the same speed.

Reference displacements ($\rho=1$)

Densities ($\rho$) are relative to the density of particles shown in part 1. For convenience, the results for the reference density (parameterized from the kinetics of the number of cases obtained before the implementation of containments measures are in France).

All evolutions assume an initial configuration based on one single infected particle (in orange).

 

Displacements at high densities ($\rho>1$)

This situation describes the kinetics when the number of contacts is increased.

$\rho=1.27$

$\rho=1.25$

$\rho=1.11$

 

Displacements at low densities ($\rho<1$)

This situation describes the kinetics when the number of contacts is lower than the reference. Lifting containment measures should be followed by a number of contacts lower than the reference. Note that the movies are accelerated when $\rho$ decreases.

$\rho=0.9$

$\rho=0.83$

$\rho=0.71$

$\rho=0.57$

 

$\rho=0.5$

$\rho=0.33$

$\rho=0.25$

$\rho=0.2$

$\rho=0.1$

One new infected particle only and rapid recovery for both particles.

$\rho=0.05$

The infected particle is shown around 1 pm, but disappears rapidly as it recovers rapidly.

$\rho=0.025$

No risk of infection.

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Olivier (day 91 after the outbreak, as counted by COVID19 Forecast - Based on these similations, it is obvious that you have to keep your social distance and apply safe barriers. For any question, send an email to the author.