The distribution of the prevalence of ocular chlamydial infection in communities where trachoma is disappearing

• Models of infectious disease disappearance should approach geometric distribution.
• Trachoma is ideal to model, as infection is disappearing in longitudinal studies.
• The geometric distribution had most parsimonious fit of those tested.
• A geometric distribution fit is encouraging, possibly implying disease elimination.

Mathematical models predict that the prevalence of infection in different communities where an infectious disease is disappearing should approach a geometric distribution. Trachoma programs offer an opportunity to test this hypothesis, as the World Health Organization (WHO) has targeted trachoma to be eliminated as a public health concern by the year 2020. We assess the distribution of the community prevalence of childhood ocular chlamydia infection from periodic, cross-sectional surveys in two areas of Ethiopia. These surveys were taken in a controlled setting, where infection was documented to be disappearing over time. For both sets of surveys, the geometric distribution had the most parsimonious fit of the distributions tested, and goodness-of-fit testing was consistent with the prevalence of each community being drawn from a geometric distribution. When infection is disappearing, the single sufficient parameter describing a geometric distribution captures much of the distributional information found from examining every community. The relatively heavy tail of the geometric suggests that the presence of an occasional high-prevalence community is to be expected, and does not necessarily reflect a transmission hot spot or program failure. A single cross-sectional survey can reveal which direction a program is heading. A geometric distribution of the prevalence of infection across communities may be an encouraging sign, consistent with a disease on its way to eradication.