SIR Modeling

Compartmental Modeling

​Discrete-time SIR modeling of infections/recovery

The model consists of individuals who are either Susceptible ([math]S[/math]), Infected ([math]I[/math]), or Recovered ([math]R[/math]).

The epidemic proceeds via a growth and decline process. This is the core model of infectious disease spread and has been in use in epidemiology for many years.

The dynamics are given by the following 3 equations.

[math]S_{t+1} = S_t - \beta S_t I_t[/math]

where;

[math]S[/math] number of susceptible individuals,

[math]I[/math] number of infected individuals.

[math]I_{t+1} = I_t + \beta S_t I_t - \gamma I_t[/math] [math]R_{t+1} = R_t + \gamma I_t[/math]