To run the Simulator:

g++ main.cpp

The SIR mathematical model is used for describing the spread of infectious diseases within a population. It divides the population into three groups:

• Susceptible (S): Individuals who are not infected but can get infected.
• Infectious (I): Individuals who are currently infected and can transmit the disease.
• Removed (R): Individuals who have either recovered or died from the disease.

The SIR model is described by the following set of differential equations:

1. Susceptible Population (S): $\frac{dS}{dt} = -\beta \frac{SI}{N}$

2. Infected Population (I): $\frac{dI}{dt} = \beta \frac{SI}{N} - \gamma I$

3. Recovered Population (R): $\frac{dR}{dt} = \gamma I$

Where $\beta$ is the transmission rate and $\gamma$ is the recovery rate.

In order to solve the differential equations, thus allowing us to know the number of susceptibles, infected, and removed individuals at a particular momment in time, I used Euler's numeric method:

1. Susceptible Population (S): ${S_{n+1}} = {S_n}-\beta {S_nI_n \Delta t}$

2. Infected Population (I): ${I_{n+1}} = {I_n}+ (\beta {S_nI_n - \gamma I_n \Delta t})$

3. Recovered Population (R): ${R_{n+1}} = {R_n} + {\gamma I_n \Delta t}$

The user can set:

• Average age of the population (affects transmission rate)
• Variant of the virus (affects transmission rate)
• Percentage of the population that is vaccinated (affects transmission rate)
• Initial number of infected individuals
• Number of days to run the simulation

For further customization, you can change the base tranmission rates for each variant in the constructor of the Population.h file.