FIG. 07
Epidemic Spread
SIR · agent-based · Contagion‹ All modelsloading model…
What's happeningFIG. 07 · Sheet 08
An agent-based SIR epidemic: every dot is a person moving in a box, coloured Susceptible (blue), Infectious (orange) or Recovered (green). Starting from three infections near the centre, an infectious person passing within the contact radius of a susceptible one can transmit; after a fixed infectious period each case recovers and becomes immune. Out of these local, random contacts emerges the classic epidemic curve — a single wave of infection that rises, peaks, then burns out as susceptibles run dry.
Parameters — how to use them
- Transmission β
- Probability of infection per contact with an infectious neighbour (0.05–1). It is the per-edge transmission rate: raise it toward 1 and the outbreak ignites fast and infects nearly everyone; drop it low and many runs fizzle before spreading, since R₀ scales with β.
- Infectious period
- How many seconds a case stays infectious before recovering (2–16 s). Longer periods give each infective more chances to transmit, raising R₀ and the final outbreak size; shorten it and infections recover before they can pass it on, helping the wave die out.
- Contact radius
- The distance (6–28 px, drawn as the orange ring around each case) within which transmission can occur. Widen it and effectively everyone is a contact, so the epidemic explodes; narrow it and spread slows to a crawl as infectives must nearly touch a susceptible to pass it on.
- Size
- Total population, 60–600 (takes effect on the next Re-seed). Larger populations give denser mixing and smoother, taller epidemic curves; smaller ones are noisier and more prone to chance burnout from the same three seeds.
- Mobility
- Movement speed multiplier for everyone who is moving (0.1×–2.2×). High mobility mixes the population fast and accelerates a sharp, early peak; lower it toward 0.1× and the infection spreads as a slow local wave instead of igniting everywhere at once.
- Distancing
- Fraction of people (0%–90%) who stay put instead of moving (set at the next Re-seed). This is the lockdown lever: push it up and most agents become stationary, fragmenting contact so the curve flattens and the peak drops — the whole point for not overwhelming a hospital.
- Re-seed outbreak
- Rebuilds the population with current settings and reignites three fresh infections, clearing the history plot. Use it to A/B test an intervention: note the peak, raise Distancing or lower Transmission β, re-seed, and compare the new peak height.
What to watch for
Watch orange bloom outward from the centre and chase the blue dots until it runs out of susceptibles and fades to green. The S / I / R readouts always sum to the population (conservation), and the epidemic curve below stacks them over time — the orange I(t) band is the wave whose height is labelled 'peak'. Flattening that peak with lower mobility, transmission, or higher distancing is the public-health money shot.