Difference between revisions of "SIR Modeling"
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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 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 | + | The dynamics are given by the following three equations; |
<!-- {{#tag:math|S_{t+1} = S_t - \beta S_t I_t }} --> | <!-- {{#tag:math|S_{t+1} = S_t - \beta S_t I_t }} --> | ||
:<math> | :<math> | ||
\begin{align} | \begin{align} | ||
− | S_{t+1} & = S_t - \beta S_t I_t | + | 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] | I_{t+1} & = I_t + \beta S_t I_t - \gamma I_t \\[6pt] | ||
R_{t+1} & = R_t + \gamma I_t | R_{t+1} & = R_t + \gamma I_t |
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 three equations;
where;
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