Stochastic challenges to interrupting helminth transmission

Abstract

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 as 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 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. The analyses based on migration confirm a relationship between the infected human migration rate per unit of time and the death rate of infective stages that are released into the free-living environment (eggs or larvae depending on the STH species) that create the reservoir of infection which in turn determines 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. : medRxiv preprint A stochastic individual-based modelFollowing past publications [12,23], the STH transmission model we introduce here is a stochastic individual-based analogue to the deterministic original given in Refs. [26,11,7]. : medRxiv preprint ∂ ∂Z G jn [Z(t), t] = λ jn Λ j (t) [Z(t) − 1] G jn [Z(t), t] , whose solution is given by Eq. (A.4) when one replaces Z(t ) − 1 with the inverted form of the equation above.

Spatial scales in human movement between reservoirs of infection

“…It was shown in Refs. [13, 14] that if the average daily rate at which reservoir pulses occur exceeds the average death rate of the infectious material in the reservoir per day, d res , then the effect of infected human migration on the transmission dynamics becomes particularly strong. By combining these two concepts above, one may derive a new and important spatial scale for reservoirs of infection which depends on the type of helminth, as well as the local geometry of locations and human movement behaviour.…”

“…(17) cannot be safely neglected and should become important to take into account when modeling the transmission dynamics (see Refs. [13, 14]). If, however, the spatial scale of the epidemiological unit is larger than , then effects from migration between reservoirs of infection may po-tentially be safely neglected.…”

“…In Ref. [14] it was shown that, to good approximation for moderate-to-large population numbers, the worm burden distributions of individuals p ( w i , t ) evolve according to the following reservoir birth-death process master equation The solution to this equation is a Poisson distribution p ( w i , t ) = Pois[ w i ; I i ( t )] with time-dependent intensity in which we have inserted the solution to Eq. (16).…”

“…Following Ref. [14], this translates into the following decomposition of the positive migratory process in Eq. (19) where is the contribution to the infectious material quantity of a focal point by an individual: a random variable with a distribution which varies between disease, but likely follows a negative binomial character in some cases.…”

“…Defining the spatial scales over which transmission should be considered is a relatively recent research area in the context of neglected tropical diseases (NTDs), where much of the effort has been focused on the development of geostatistical methods for each disease in turn [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. In particular, mathematical models of helminth transmission have only recently begun to incorporate the dynamical effects of human movement between reservoirs of infection [9, 12, 13, 14].…”