The distribution of district-level leprosy incidence in India is geometric-stable, consistent with subcriticality

Mathematical models predict that the community-level incidence of a controlled infectious disease across a region approaches a geometric distribution. This could hold over larger regions, if new cases remain proportional to existing cases. Leprosy has been disappearing for centuries, making an excellent candidate for testing this hypothesis. Here, we show the annual new case detection rate of leprosy in Indian districts to be consistent with a geometric distribution. For 2008–2013, goodness-of-fit testing was unable to exclude the geometric, and the shape parameter of the best fit negative binomial distribution was close to unity (0.95, 95% CI 0.87–1.03). Ramifications include that a district-level cross-sectional survey may reveal whether an infectious disease is headed towards elimination, that apparent outliers are expected and not necessarily representative of program failure, and that proportion 1/e of a small geographical unit may not meet a control threshold even when a larger area has. Keywords: Leprosy, Geometric distribution, Elimination, Mathematical mode