Epidemiology API

Epidemiology-basics maths as an API, computed locally and deterministically. The herd-immunity endpoint computes the herd-immunity threshold HIT = 1 − 1/R0 — the immune fraction of a population at which an outbreak can no longer sustain itself — from the basic reproduction number R0, and adjusts for an imperfect vaccine by dividing by its efficacy, so a disease with R0 = 3 needs about 67 % immune (74 % vaccinated with a 90 %-effective vaccine) while measles at R0 ≈ 15 needs about 93 %. The r-effective endpoint computes the effective reproduction number Re = R0 · susceptible fraction and flags whether the epidemic is growing (Re > 1) or shrinking. The final-size endpoint solves the final-epidemic-size equation Z = 1 − e^(−R0·Z) for the eventual attack rate of an unmitigated SIR epidemic — about 80 % at R0 = 2. The doubling-time endpoint gives the case-doubling time from a growth rate, or from R0 and the serial interval. Fractions are 0–1 and percentages are derived. Everything is computed locally and deterministically, so it is instant and private. Ideal for public-health, epidemiology-education, dashboard, science-communication and outbreak-planning app developers, herd-immunity and reproduction-number tools, and health software. Simple compartmental relations for education and planning, not a substitute for full epidemiological modelling. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 4 endpoints. This is epidemiology basics; for population-genetics Hardy-Weinberg use a genetics API.