Estimating the elimination feasibility in the 'end game' of control efforts for parasites subjected to regular mass drug administration: Methods and their application to schistosomiasis

Progress towards controlling and eliminating parasitic worms, including schistosomiasis, onchocerciasis, and lymphatic filariasis, is advancing rapidly as national governments, multinational NGOs, and pharmaceutical companies launch collaborative chemotherapeutic control campaigns. Critical questions remain regarding the potential for achieving elimination of these infections, and analytical methods can help to quickly estimate progress towards-and the probability of achieving-elimination over specific timeframes. Here, we propose the effective reproduction number, R-eff, as a proxy of elimination potential for sexually reproducing worms that are subject to poor mating success at very low abundance (positive density dependence, or Allee effects). R-eff is the number of parasites produced by a single reproductive parasite at a given stage in the transmission cycle, over the parasite's lifetime-it is the generalized form of the more familiar basic reproduction number, R-0, which only applies at the beginning of an epidemic-and it can be estimated in a 'modelfree' manner by an estimator ('epsilon'). We introduce epsilon, demonstrate its estimation using simulated data, and discuss how it may be used in planning and evaluation of ongoing elimination efforts for a range of parasitic diseases.