How this calculator works
The deterministic SIR equations track a closed, randomly mixing population with constant rates and lasting removal from susceptibility. You enter R0 and the mean infectious period rather than selecting an infection with a fixed preset. The model uses fourth-order Runge-Kutta integration with smaller internal steps than the reporting interval. Expected counts may be fractional. Births, deaths, reinfection, latency and interventions are absent. The result is an estimate for information only and is not medical advice.
Formula
dS/dt = -beta S I/N; dI/dt = beta S I/N - gamma I; dR/dt = gamma I. gamma = 1 / mean infectious period; beta = R0 gamma. S + I + R = N.
Worked example
With 1000 people, 90% susceptible, 10% infectious, R0 = 0 and a five-day infectious period, no new infections occur. After five days I = 100/e = 36.7879 and R = 63.2121, while S stays 900.
Advertisement
Frequently asked questions
Is this a current COVID-19 forecast?
No. It is a teaching model with user-supplied assumptions. Calibration, uncertainty and changing population behaviour are not included.
Why are new removals different from new infections?
Infections transfer people from S to I; removals transfer them from I to R after an infectious period. They are different flows.
Why use a table instead of a chart?
The calculator engine supports tables. Each row reports the state and interval flows; up to 500 rows are allowed.