Mass drug administration: The importance of synchrony

Mass drug administration, a strategy in which all individuals in a population are subject to treatment without individual diagnosis, has been recommended by the World Health Organization for controlling and eliminating several neglected tropical diseases, including trachoma and soil-transmitted helminths. In this article, we derive effective reproduction numbers and average post-treatment disease prevalences of a simple susceptible-infectious-susceptible epidemic model with constant, impulsive synchronized and non-synchronized drug administration strategies. In the non-synchronized model, the individuals in the population are treated at most once per period and their treatment times are uniformly distributed. Mathematically, the set of pulses for the non-synchronized model has the cardinality of the continuum. We show that synchronized and constant strategies are, respectively, the most and least effective treatments in disease control. Elimination through synchronized treatment is always possible when adequate drug efficacy and coverage are fulfilled and sustained. For a strategy with multiple rounds of synchronized treatment per period, the average post-treatment prevalence is irrelevant what the time differences between treatments are, as long as there are the same number of treatments per period.