Abstract
The existence of multiple stable equilibria in models of parasitic helminth transmission was a ground-breaking discovery over 30 years ago. An implication of this discovery, that there is a level of infection below which transmission cannot self-sustain called the transmission breakpoint, has in part motivated the push towards the elimination of many human diseases caused by the multiple species of helminth worldwide. In the absence of vaccines, the predominant method in this push towards elimination is to repeatedly administer endemic populations with anthelmintic drugs, over several treatment rounds, in what has become to be known as mass drug administration (MDA). MDA will inevitably alter the distribution of parasite burdens among hosts from the baseline distribution, and significantly, the location of the transmission breakpoint is known to be dependent on the level of aggregation of this distribution-for a given mean worm burden, more highly aggregated distributions where fewer individuals harbour most of the burden, will have a lower transmission breakpoint. In this paper, we employ a probabilistic analysis of the changes to the distribution of burdens in a population undergoing MDA, and simple approximations, to determine how key aspects of the programmes (including compliance, drug efficacy and treatment coverage) affect the location of the transmission breakpoint. We find that individual compliance to treatment, which determines the number of times an individual participates in mass drug administration programmes, is key to the location of the breakpoint, indicating the vital importance to ensure that people are not routinely missed in these programmes.