## SIR Modeling

The SIR classical model is mainly used in the field of infectious diseases to predict future trends in the number of infections.

**S[t]** denotes **susceptible** susceptible population

**I[t]** denotes **infected** population already infected

**R[t]** indicates **recovered** recovered population

Reference:

MathWorld:

### Kermack-McKendrick Model

The original Kermack-McKendrick model was designed to account for changes in the number of people infected over time, like the plague that occurred in 1665-1666 and the cholera that occurred in 1865.
The model assumes that the total population is **fixed**, that the incubation period for infectious diseases is instantaneous, that the duration of infection is the same as the disease cycle, and that the population is assumed to be non-differentiable, without differences by gender or race.

The model uses three nonlinear ordinary differential equations:

**beta**denotes*infection rate*infection rate**gamma**denotes*recovery rate*recovery rate**i**indicates infected population**r**indicates recovered population**s**indicates susceptible population

Pre-set values: beta = 20%, gamma = 15%, i(0) = 0.1, r(0) = 0, s[0] = 10

Modelica source code

model model SIRModel parameter Real beta = 0.2; parameter Real gamma = 0.15; Real i; Real r; Real s; initial equation s = 10; i = 0.1; r = 0; equation der(s) = (-1) * beta * i * s; der(i) = (-1) * gamma * i + beta * i * s. der(i) = (-1) * gamma * i + beta * i * s; der(r) = gamma * i; end SIRModel;

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Model prediction graph:
![SIRModelPlot](/images/mathematica/SIRModelPlot.png)
SystemModeler prediction plot
![SIRModelPlot2](/images/mathematica/SIRModelPlot2.png)
## SEIR Model ##
Doing
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