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Simulates the basic compartmental SIR (Susceptible-Infected-Recovered) epidemic model using the standard discrete-time difference equations taught in mathematical epidemiology textbooks: S(t+1) = S(t) - beta S(t) I(t)/N, I(t+1) = I(t) + beta S(t) I(t)/N - gamma I(t), R(t+1) = R(t) + gamma I(t). This is a simplified, purely mathematical educational model with well-known simplifying assumptions (homogeneous mixing, constant beta/gamma, no births/deaths/reinfection) — it is an educational illustration of epidemic dynamics, not a real outbreak forecast or public-health prediction.
How it works
Enter the total population, initial infected count, transmission rate (beta), recovery rate (gamma), and number of days to simulate. The tool iterates the SIR difference equations day by day and reports the peak infected count, the day it occurs, and the final S/I/R breakdown.
- Enter total population (N).
- Enter initial infected count.
- Enter transmission rate (beta).
- Enter recovery rate (gamma).
- Enter simulate for (days).
- Click Calculate to see your results.
Examples
Population 10,000, 10 initial infected, beta 0.3, gamma 0.1, 100 days
The model projects an epidemic curve where the infected count rises to a peak before declining as the susceptible pool shrinks and recoveries accumulate — S+I+R remains constant at 10,000 throughout.
Who should use it
- Mathematical epidemiology education.
- Understanding how R0, transmission rate, and recovery rate shape an epidemic curve.
Industry applications
- Public health education
- Applied mathematics coursework
Advantages
- Uses the standard, well-established discrete-time SIR equations.
- Conserves total population exactly across all time steps.
Limitations
- Assumes homogeneous mixing and constant rates — real epidemics have neither.
- Does not model births, deaths, reinfection, or interventions changing over time.
Common mistakes to avoid
- Treating the projected numbers as a real-world forecast rather than an educational illustration of model dynamics under fixed assumptions.
Best practices
- Try varying beta and gamma to see how the peak size and timing change — this is the main educational value of the model.
Tips
- The basic reproduction number R0 = beta/gamma is the key summary statistic: values above 1 predict growth, values below 1 predict decline, in this simplified model.