SIR Epidemic Model
The Kermack-McKendrick SIR model is a fundamental compartmental model in epidemiology. It describes the spread of an infectious disease through a population divided into three compartments: Susceptible, Infectious, and Recovered. Explore how changes in transmission and recovery rates alter the course of an epidemic.
The Equations
The SIR model equations dictate the flow of individuals between the three compartments:
Where $N = S + I + R$ is the total population size.
- $\beta$: The transmission rate, or the expected number of contacts per person per time multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject.
- $\gamma$: The recovery rate, where $1/\gamma$ is the average duration of infection.
Basic Reproduction Number
A key concept in epidemiology is the basic reproduction number, $R_0 = \beta / \gamma$. It represents the expected number of secondary cases produced by a single infectious individual in a completely susceptible population. If $R_0 > 1$, an epidemic will occur.