SIRClassical epidemic model by Kermack and McKendrick |
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Diagram
Information
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The SIR model is a classical approach in mathematical epidemiology to study the spread of infectious diseases. The model goes back to William Ogilvy Kermack and Anderson Gray McKendrick [23] and is also called Kermack-McKendrick-Model.
The whole population is separated into three stocks(→modelOutput):
- The Susceptible (S) population is not immune and may be infected.
- The Infected (I) population has been infected and is contagious.
- The Removed (R) population can neither be infected nor spread the disease.
As in the example →SimpleProductionChainIII we are using the →Diffusion component to model social diffusion, e.g., transmission by close contact. The transmissionRate (β in the mathematical literature) is also sometimes called the effective contact rate which helps to understand why we have set the adoptionFraction to 1in the Diffusion component.
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Notes
- As in the example →SimpleProductionChainIII we need to use an expandable connector (
inputDiffusion) at the scope of the model to establish connections for inputs tobecoming_infectedin compliance with Modelica specifications. SystemModeler will assist connections with a drop down list making this rather convenient.
Parameters (3)
| baseReproductionNumber |
Value: 2.5 Type: Dimensionless Description: Value of constant output (R0.value) |
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| infPeriod |
Value: 432000 Type: Time (s) Description: Length of the infectious perid (infectiousPeriod.value) |
| n |
Value: 3 Type: Integer Description: Order of the exponential delay (infected.n) |
Connectors (2)
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modelOutput |
Type: ModelOutput Description: The model's main output |
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inputDiffusion |
Type: DataInPort Description: Collected (named) input for the infection process |
Components (9)
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modelSettings |
Type: ModelSettings Description: Setting important global variables within a model |
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susceptible |
Type: MaterialStock Description: Population in the susceptible stage of the disease |
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removed |
Type: MaterialStock Description: Reservoir that cannot be drained below zero |
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infected |
Type: DelayN Description: Population in the infectious stage of the disease |
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becoming_infected |
Type: Diffusion Description: The infection is spread by a process of social diffusion |
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being_removed |
Type: OutflowDynamicStock Description: Outflow from a dynamic stock—the rate is set by the stock |
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infectiousPeriod |
Type: ConstantConverterTime Description: Time interval during which an individual is infectious |
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R0 |
Type: ConstantConverter Description: Basic reproduction number for the infectious disease |
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transmissionRate |
Type: Division Description: Effective contact rate |
Revisions
- Adjusted
modelSettingsand modified plot in v2.0.0.