Macro-parasite transmission in dynamic seasonal environment: Basic Reproductive Number, endemicity, and control

Seasonality of transmission environment, which includes snail populations and habitats, or human-snail contact patterns, can affect the dynamics of schistosomiasis infection, and control outcomes. Conventional modeling approaches often ignore or oversimplify it by applying seasonal mean formulation. Mathematically, such averaging is justified when model outputs/quantities of interest depend linearly on input variables. That is not generally the case for macroparasite transmission models, where model outputs are nonlinear functions of seasonality fashion. Another commonly used approach for Schistosomiasis modeling is a reduction of coupled human-snail system to a single human equation, via quasi-stationary snail (intermediate host) dynamics. The basic questions arising from these approaches are whether such seasonal averaging and intermediate host reduction are suitable for highly variable/seasonal environments, and what implications these methods have on models predictive potential of control interventions. Here we address these questions by using a combination of mathematical analysis and numerical simulation of two commonly used models for macroparasite transmission, MacDonald (MWB), and stratified worm burden (SWB) snail-human systems. We showed that predictions from seasonal averaging models can depart significantly from those of quasi-stationary models. Typically, seasonality would lower endemicity and sustained infection, vs. stationary system with comparable transmission inputs. Furthermore, discrepancies between the two models ( seasonal and its stationary mean) increase with amplitude (or variance) of seasonality. So sufficiently high variability can render infection unsustainable. Similar discrepancies were observed between coupled and reduced single host models, with reduced model overpredicting sustained endemicity. Seasonal variability of transmission raises the question of optimal control timing. Using dynamic simulation, we show that optimal timing of repeated MDA is about half season past the snail peak, where snail population attains its minimal value. Compared to sub-optimal timing, such strategy can reduce human worm burden by factor 2 after 5-6 rounds of MDA. We also extended our models for dynamic snail populations, which allowed us to study the effect of repeated molluscicide, or combined strategy (MDA + molluscicide). The optimal time for molluscicide alone is the end or the start of season, and combined strategy can give additional reduction, and in some cases lead to elimination. Overall, reduced sustainability in seasonal environment makes it more amenable to control interventions, compared to stationary environment.