Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

Assessing Onchocerciasis Subcriticality from Pre-Intervention Cross-Sectional Surveys

Elimination of an infectious disease requires subcritical transmission, or a reproductive number less than one, and can be assessed with cross-sectional surveys conducted by neglected tropical disease programs. Here, we assess the distribution of onchocerciasis prevalence taken from surveys across sub-Saharan Africa before the initiation of ivermectin in mass drug administrations. Pre-intervention nodular palpation cross-sectional surveys were available from 15 countries in the Expanded Special Project for Elimination of Neglected Tropical Diseases (ESPEN) database. We determined whether the distribution of the prevalence over communities in an area was consistent with a geometric distribution, which previous studies have suggested indicates a subcritical disease. If not, we fitted a negative binominal distribution (hypothetically supercritical) or a mixture of two distributions: geometric (hypothetically subcritical) and Poisson (hypothetically supercritical). The overall distribution of community-level onchocerciasis prevalence estimates from the ESPEN dataset from 2005 to 2014 was not consistent with a geometric distribution. By contrast, data from several countries and parts of countries were consistent with the geometric distribution, for example, some areas within Nigeria and Angola. Even if the geometric distribution suggested pre-intervention subcriticality in more localized geographical areas, our model using pooled survey data of all geographic areas suggests that the entire pre-intervention prevalence does not fit a geometric distribution. Further work will be required to confirm the significance of a geometric distribution for onchocerciasis.