Epidemic (Simplified model)

THIS SIMULATION IS FOR EDUCATIONAL PURPOSES ONLY!

The parameters used and the curves observed are not characteristic of a particular virus. Our goal is to provide teachers with a qualitative tool to illustrate how a virus spreads and how to fight an epidemic.

In no way can this simulation be used as justification or evidence. A simulation is an approximation of reality. The parameters that characterize the spread and the dangerousness of an epidemic are numerous. These parameters are as much scientific as they are social. Each community is therefore different with regard to the spread of the virus and there is no single answer to fight it. The parameters for this simulation are explained below, 

In the fight against the spread of a virus, it is fundamental to remember certain scientific facts:

• Our skin is an effective barrier against the virus. It is mainly through the mouth, nose or eyes that it can enter our body. A coronavirus is a type of virus that has a lipid envelope which protects its genetic material. Washing your hands with soap and not putting your hands on your face are effective "barrier gestures".
• A virus hardly survives outside its host organism. It is transmitted by micro-droplets. Confinement and/or social distancing greatly limits its transmission.
• An infected organism mainly defends itself with its own immune system. When a majority of the population has achieved immunity, either by vaccination or after recovery, and if the immunity is durable enough, the epidemic stabilizes at a low level or subsides.

In the absence of a vaccine, victory against an epidemic therefore requires strict individual discipline (hygiene, confinement, social distancing), which is very difficult to implement on a societal scale, especially over time.

For the above simulation, we used the SIR model (Susceptible-Infected-Recovered):

• S (pink): The "Susceptible" state characterizes a healthy individual not carrying the virus.
• I (red): The "Infected" state characterizes a contagious individual. The latter can be symptomatic (fever, cough, pain ...) or asymptomatic.Being asymptomatic, he may go under the radar of many tests.
• R (gray): The "restored" state characterizes a healed individual. The latter is no longer contagious and benefits from a more or less durable immunity preventing the virus from spreading.

Death cases are not considered in this simulation. It constitutes a percentage of the "I" population ( < 1% for seasonal flu, > 3% for Covid-19, > 15% for smallpox).

The simulation applies the following algorithm to one fixed population of 800 individuals

The distance between each individual is calculated. If the distance between two individuals "I" and "S" is less than a certain proximity threshold, we apply a probability P of contagion which moves individual "S" to "I".

In the absence of "barrier gestures", the evolution in the early stages clearly expresses a very rapid exponential growth in the number of infected (I). Health policies are desperately seeking to limit this growth in order to protect its health system. However, an exponential function grows so fast that decisions must be made very quickly.

Political measures are necessarily collective because the presence of a single "I" individual can, over time, contaminate the entire population. This may involve vaccination, containment, or quarantine of all travelers.

This educational simulation allows certain qualitative conclusions to be drawn :

• In the absence of a vaccine, confinement or quarantine measures for travelers have significant effects, especially if applied very early.
• A vaccination campaign is only effective beyond a certain percentage of the population treated.
• Until the disease is eradicated, an epidemic can spread several times within the same population.

The last point explains the difficulty for governments to organize a "de-confinement".

eduMedia has made a comprehensive interactive report on the topic of the epidemic. Click “Virus, vaccine, viral subject” to access it.

Bibliography:

• eduMedia SEIR model epidemy
• Vidéo "Exponential Growth" de 3Blue1Brown (Grant Sanderson)
• Site Complexity Explorable (Dirk Brockmann)
• Epidemic Modeling 101: "Or why your CoVID-19 exponential fits are wrong" (Bruno Gonçalves)
• Epidemic Modeling 102: "All CoVID-19 models are wrong, but some are useful" (Bruno Gonçalves)
• SIR model simulation commented Vidéo .