The Compartmental Approach

The SIRD model tracks four compartments — Susceptible, Infected, Recovered, Deceased — with two daily flows: susceptible → infected at rate β·S·I/N, and infected → recovered or deceased at rate γ. Simple as it is, it reproduces the classic epidemic curve: exponential growth, a peak, then decay as the susceptible pool depletes.

R₀ and Herd Immunity

R₀ = β ÷ γ tells you whether an outbreak grows (R₀ > 1) or dies out (R₀ < 1). Herd immunity — the share of the population that must be immune to stop spread — is approximately 1 − 1/R₀. For R₀ = 3 that is 67%; for R₀ = 2, 50%.

What This Model Omits

Real outbreaks include age structure, spatial spread, seasonality, and — most importantly — behavior change and intervention. This calculator is a teaching tool for understanding dynamics (why flattening the curve works, what CFR changes do). It is not a real-outbreak forecast.