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.
Highlights
A defining feature of the epidemiology of macroparasites is that the parasite burden of an individual is positively correlated to infectiousness and morbidity [1]
We focus on the expected effect of mass drug administration (MDA) on a population of helminth parasites which prior to intervention is distributed as a negative binomial among its human host population
The post-MDA distribution for those people who receive treatment in a single round is a negative binomial with mean m0(1 − ε) and aggregation k0. (This result or one very close using moments is in Anderson & May, 1991, and detailed in Anderson et al 2016, based on compounding distributions with different means to represent either age, exposure to infection or acquired immunity [1,12].) Applying this reasoning inductively, and ignoring transmission dynamics between MDA rounds, we find that the distribution after n rounds of MDA is
Summary
A defining feature of the epidemiology of macroparasites is that the parasite burden of an individual is positively correlated to infectiousness and morbidity [1]. Controlling the morbidity of these diseases is primarily performed by large-scale deworming programmes employing anthelmintic drugs, referred to as mass drug administration (MDA), in which drugs are supplied to whole communities at a given frequency (once a year or more or less frequently depending on the intensity of transmission as measured by the basic reproductive number R0) to suppress the prevalence and average intensity of infection These interventions may have a major effect on the distribution of worm burden, and may, in some circumstances, invalidate the common assumption that the distribution is well characterized by a negative binomial distribution. We use our derived values for the mean and aggregation after successive MDA rounds to determine if it is possible to reach the transmission breakpoint for different coverages and levels of non-compliance
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