SIR Spread Model, explained.
The SIR model divides a population into susceptible, infectious, and recovered groups to explore how transmission and recovery can shape an epidemic.
Why it happens
New infections depend on contact between susceptible and infectious people, while recovery moves people out of the infectious group. An outbreak can slow as the susceptible pool shrinks, even if the transmission parameter itself stays fixed.
Spread and recovery compete as people move between susceptible, infectious and removed groups.
Read the result
Compare new movement between groups with the number currently infectious. Change transmission and recovery separately, and remember that these curves describe a simplified closed population rather than an actual forecast.
A worked example
A spreading infection in a closed group
Nearly everyone starts susceptible, with a small infectious group and no new arrivals.
Transmission initially increases infections. Later, more people have recovered and fewer remain susceptible.
The infectious group can peak and decline because the conditions for further spread change through the outbreak itself.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A closed population starts 99% susceptible and 1% infectious. Each discrete day, new infections are βSI and recoveries are γI, with fractions of the whole population; values are clamped to available compartments. The plot runs 80 days.
Where this idea is useful
A practical use
Understand why the same starting cases can produce different trajectories under different contact assumptions.
A common misconception
“A downward curve means the organism became less transmissible.”
In this model, susceptible depletion can cause decline without a change in the transmission parameter. Real outbreaks have many additional influences.
What this explanation leaves out
- No age structure, immunity loss, births, geography or behavior changes; this is educational and not a health forecast.
Are these curves suitable for predicting my local outbreak?
No. They omit contact networks, changing behavior, testing, age differences, and other important factors. They illustrate feedback, not a calibrated local forecast.
Is a changing outcome caused by a changed parameter or by a changing population state?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.