Interactive SIR epidemic simulator — tweak parameters, see the curve
🦠
No simulation run yet
Fill in the parameters above and press Run Simulation to model the epidemic curve.
SIR Population Curves Over Time
180 days · 100,000 population
S
I
R
S
I
R
S
I
R
S
I
R
Day 0Day 30Day 60Day 90Day 120Day 150Day 180
Peak Infected—awaiting run
Peak Day—awaiting run
Final Recovered—awaiting run
Final Susceptible—awaiting run
Macro Epidemic Lens
β = 0.30 · γ = 0.05
With R₀ = β/γ = 6.0, this scenario is highly transmissible — herd immunity requires ~83% coverage.
At 20% vaccination, roughly 64,000 susceptible individuals remain exposed. Without additional intervention the infected compartment will climb steeply before recovery outpaces transmission. The classic flu-season shape features a sharp peak around day 40–60 followed by a long recovery tail that flattens near day 150.
Containment factors
20% vaccination reduces initial susceptible pool
Recovery rate γ = 0.05 means ~20-day infectious period
Population immunity grows as wave passes
Amplifying factors
High β = 0.30 drives rapid person-to-person spread
R₀ = 6.0 far exceeds the epidemic threshold of 1
80% of population unvaccinated at simulation start
Intervention Lens
Vaccination Impact
Each 10% increase in vaccination shrinks peak infected by an estimated 8–12% and delays the peak day by roughly a week.
Raising vaccination coverage from 20% to 60% would push effective R₀ below 2.5, dramatically flattening the curve and reducing total deaths. The simulation re-runs instantly — adjust the vaccination % field and press Run Simulation to explore the counterfactual.
Outlook
If transmission rate β drops below 0.07 (through NPIs like masking + distancing), the epidemic self-extinguishes within 60 days without reaching peak. Combine β reduction with ≥40% vaccination to stay below healthcare capacity thresholds.
Projected Epidemic Timeline
Day 1
Seed event
Single infectious individual enters the susceptible population of 80,000 (post-vaccination).
Day 15
Exponential growth phase
Infected count doubles every 3–4 days as susceptible pool remains large.
Day 45
Peak infected
Epidemic apex — maximum simultaneous infections. Recovery now outpaces new cases.
Day 90
Declining wave
Infected compartment falls rapidly; recovered compartment approaches final plateau.
Day 180
Endemic equilibrium
Simulation ends. Final susceptible, infected, and recovered stocks are stable.
What is the SIR model?
SIR divides a fixed population into three compartments: Susceptible (never infected), Infected (currently contagious), and Recovered (immune). Two rates drive the dynamics — β (transmission) controls how fast S→I, γ (recovery) controls how fast I→R.
How does vaccination % affect the model?
Vaccination removes individuals from the susceptible pool at simulation start, effectively reducing the initial S₀ to Population × (1 − vax%). This directly reduces R_effective = R₀ × (S₀/N), slowing or preventing epidemic takeoff.
What does R₀ = 6.0 mean?
R₀ is the basic reproduction number — the average number of secondary infections caused by one case in a fully susceptible population. R₀ = β/γ = 0.30/0.05 = 6.0. Values above 1 sustain an epidemic; values below 1 cause it to die out.