This application simulates the dynamics of the spread of epidemics and pandemics using an interacting particle model.

People are represented by balls that interact with each other and can transmit diseases from one person to another.

There are six statuses:

• Not infected
• Asymptomatic (infected without symptoms)
• Infected with mild symptoms
• Infected with severe symptoms
• Dead
• Retrieved

Buttons:

• Starts or pauses the simulation.
• Restarts the simulation.
• Configures simulation parameters: probability of contagion, number of people, type of movement, etc.

This application simulates the dynamics of the spread of infectious diseases based on a model similar to SIR - Susceptible, Infected and Recovered.

First, the particles are drawn with random positions and velocities.

The initial condition is:

• 1 person is infected, without symptoms (patient zero).
• N-1 people are not infected.

Each interaction between particles, which corresponds to the superposition of two balls, can lead to the transmission of an infected person to an uninfected person.

If an infection occurs, there are three types of situations: infected without symptoms, with mild symptoms and asymptomatic. We consider that even asymptomatic people can transmit the disease.

Those infected with severe symptoms have their speeds reduced to zero, representing a hospital stay.

After a certain period of time, asymptomatic and infected people with mild symptoms recover. They become immune to new contagions.

After the same period of time, those infected with severe symptoms may die or recover, also acquiring immunity.

Models:

• Ideal gas: particles perform uniform rectilinear movements.
• Random walk: particles perform movements whose direction changes at every instant, in a probabilistic way.

Border types:

• Closed: particles collide elastically with the four walls. In this case, the evolution of the epidemic depends greatly on the initial position of patient zero.
• Open: particles that travel in a certain direction end up returning in the opposite direction. In this case, the evolution of the epidemic is independent of the initial position of patient zero.

Read more: