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]
\begin{align}
S_{t+1} & = S_t - \beta S_t I_t) \\[6pt]
I_{t+1} & = I_t + \beta S_t I_t - \gamma I_t \\[6pt]
R_{t+1} & = R_t + \gamma I_t
\end{align}
[/math]
where;
[math]S[/math] number of susceptible individuals,
[math]I[/math] number of infected individuals,
[math]R[/math] number of recovered individuals,
[math]\beta[/math] the average number of contacts per person per time,
[math]\gamma[/math] the transition rate.
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