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

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.