Stochastic challenges to interrupting helminth transmission

Predicting the effect of different programmes designed to control both the morbidity induced by helminth infections and parasite transmission is greatly facilitated by the use of mathematical models of transmission and control impact. In such models, it is essential to account for the many sources of uncertainty - natural, or otherwise - to ensure robustness in prediction and to accurately depict variation around an expected outcome. In this paper, we investigate how well the standard deterministic models match the predictions made using individual-based stochastic simulations. We also explore how well concepts which derive from deterministic models, such as 'breakpoints' in transmission, apply in the stochastic world. Employing an individual-based stochastic model framework we also investigate how transmission and control are affected by the migration of infected people into a defined community. To give our study focus we consider the control of soil-transmitted helminths (STH) by mass drug administration (MDA), though our methodology is readily applicable to the other helminth species such as the schistosome parasites and the filarial worms. We show it is possible to theoretically define a 'stochastic breakpoint' where much noise surrounds the expected deterministic breakpoint. We also discuss the concept of the 'interruption of transmission' independent of the 'breakpoint' concept where analyses of model behaviour illustrate the current limitations of deterministic models to account for the 'fade-out' or transmission extinction behaviour in simulations. Our analysis of migration confirms a relationship between the critical infected human migration rate scale (i.e., order of magnitude) per unit of time and the death rate of infective stages that are released into the free-living environment. This relationship is shown to determine the likelihood that control activities aim at chemotherapeutic treatment of the human host will eliminate transmission. The development of a new stochastic simulation code for STH in the form of a publicly-available open-source python package which includes features to incorporate many population stratifications, different control interventions including mass drug administration (with defined frequency, coverage levels and compliance patterns) and inter-village human migration is also described.