Susceptible Infected Recovered (SIR) Model Simulator

Description

Simulation of the SIR model written in C#. Writes per day outputs to CSV for easy ingestion into a visualizer.

Compartments

• Susceptible: The population of people that are suceptible to infection.

• Infected: The population of people that are actively infected and infectious.

• Recovered: The population of people that have recovered from the infection.

Population Delta Equations

New Susceptible Population

newS = previousState.S + (resusceptibleRate * previousState.R - infectionRate * previousState.I * previousState.S);

• 'resusceptibleRate * previousState.R': Rate at which people enter the Susceptible population from the Recovered population due to loss of immunity

• '- infectionRate * previousState.I * previousState.S': Rate at which people leave the Susceptible population and enter the infected population due to infection

New Infected Population

newI = previousState.I + (infectionRate * previousState.I * previousState.S - recoveryRate * previousState.I);

• 'infectionRate * previousState.I * previousState.S': Rate at which people enter the Infected population from the Susceptible population due to infection.

• '- recoveryRate * previousState.I': Rate at which people leave the Infected population and enter the Recovered population due to recovery.

New Recovered Population

newR = previousState.R + (recoveryRate * previousState.I - resusceptibleRate * previousState.R);

• 'recoveryRate * previousState.I': Rate at which people enter the Recovered population from the Infected population due to recovery.

• '- resusceptibleRate * previousState.R': Rate at which people leave the Recovered population and enter the Susceptible population due to loss of immunity.

Values are normalized to force values to sum to ~99% at the end of each iteration. This prevents compounding floating point multiplication errors.

double sum = newS + newI + newR;
newS /= sum;
newI /= sum;
newR /= sum;

Usage

SIR-Model.exe -d 100 -i 0.2 -r .1 -s .05 -S 0.99 -I 0.01 -R 0.0 -o results.csv

Model Inputs

Input Parameter	Description	Default Value
-d, --days	Number of days the simulation runs for.	100
-i, --infectionRate	Rate at which susceptible become infected.	0.0
-r, --recoveryRate	Rate at which infected people recover from the infection.	0.0
-s, --resusceptibleRate	Rate at which recovered people lose their immunity and become susceptible.	0.0
-S, --initialSusceptible	Initial susceptible population.	0.0
-I, --initialInfected	Initial infected population.	0.0
-R, --initialRecovered	Initial recovered population.	0.0
-o, --outputFile	Path to the simulation output file.	"output.csv"

Model Limitations

• The model does not consider natural birth and death rates within the population.
• It does not account for the mortality rate associated with the disease.
• Similar to the typical SIR model, it assumes a homogeneously mixed population.