SIR Block

A compartmental epidemiological model representing Susceptible, Infectious, and Recovered populations.

Description

The SIR model is a classic epidemiological model that describes the transmission of a contagious disease through a population. It divides the population into three compartments: Susceptible, Infectious, and Recovered.

Mathematical Model

dS/dt = -β*S*I/N, dI/dt = β*S*I/N - γ*I, dR/dt = γ*I

The model is defined by a system of three ordinary differential equations (ODEs):

$$\frac{dS}{dt} = -\frac{\beta \cdot S \cdot I}{N}$$ $$\frac{dI}{dt} = \frac{\beta \cdot S \cdot I}{N} - \gamma \cdot I$$ $$\frac{dR}{dt} = \gamma \cdot I$$

Where:

• $S$: Susceptible population
• $I$: Infectious population
• $R$: Recovered population
• $N = S + I + R$: Total population
• $\beta$: Effective transmission rate
• $\gamma$: Recovery rate (inverse of infectious period)

Parameters

beta ($\beta$)

The effective contact rate. Higher values lead to faster spread.

• Default: 0.3
• Tooltip: Effective contact rate (contacts per day)

gamma ($\gamma$)

The recovery rate. $1/\gamma$ represents the average infectious period.

• Default: 0.1
• Tooltip: Inverse of the infectious period (1/days)

initial_s

The number of susceptible individuals at the start of the simulation.

• Default: 990

initial_i

The number of infectious individuals at the start of the simulation.

• Default: 10

Ports

s, i, r (Outputs)

The current population counts for each compartment.

See Also

• LogisticGrowth: For population growth limited by resources.
• PredatorPrey: For interaction between two different populations.
• Stock: The internal components of the SIR model are essentially Stocks.