Fig 1.
An Reff profile with equilibria noted at both low (unstable; Wbp) and high (stable; Weq) parasite burdens. Between these equilibria lies a point of parasite burden (Wpeak) where intense transmission is expected (transmission being proportional to the value of Reff) due to minimized influence of restrictive negative density dependence and facilitation of transmission through amplified positive density dependence. The critical influence of positive density dependence on expected values of Reff at low worm burdens (solid line) and its deviation from expected values in the absence of positive density dependence (dashed line), where Reff → R0, is also shown.
Table 1.
Model parameters and state variables, their symbols, and values along with their literature basis.
Fig 2.
BBR profile reflecting key equilibria in relation to population parasite burden.
The BBR profile for the PDD (a, solid line) and PDD-free (a, dashed line) models. Note the symmetry with the Reff profile shown in Fig 1, including the location of key equilibria at the breakpoint (Wbp) and endemic equilibrium (Weq) where Reff and BBR = 0. Also shown is the rate of change of worm burden, (b), across log-transformed worm burden, W, for the PDD (solid line) and PDD-free (dashed line) models. At low values of W (b, inset), the models diverge as transmission in the PDD model (solid lines) is restricted by reduced mating probability leading to
< 0 below the breakpoint, Wbp.
Fig 3.
Influence of PDD on key model outputs estimated with worm burden.
(a) Worm burden profiles derived from the PDD model (black line) and PDD-free model (red line) during 20 rounds of simulated annual MDA followed by 40 years with no intervention (the worm burden trajectory from the PDD-free model is shifted two months along the axis to improve clarity). In the presence of PDD, W remains at 0 even after releasing MDA as it has been suppressed below Wbp (a), while a lack of PDD allows W to rebound back to pre-MDA levels once MDA stops. (b) Mean BBR values of 100 model runs across 20 annual treatment rounds with error bars indicating standard deviation. (c) The elimination feasibility coefficient, ε, for the PDD model (black bars) and the PDD-free model (red bars) across each round of MDA. Error bars represent standard deviation.
Fig 4.
Influence of PDD on key model outputs estimated with prevalence.
(a) Prevalence profiles derived from the PDD model (black line) and PDD-free model (red line) during 20 rounds of simulated annual MDA followed by 40 years with no intervention (the prevalence trajectory from the PDD-free model is shifted two months along the axis to improve clarity). In the presence of PDD, prevalence remains at 0% even after releasing MDA (a), while a lack of PDD allows the prevalence to rebound back to pre-MDA levels once MDA stops. (b) Mean prevalence-based BBR values of 100 model runs across 20 annual treatment rounds with error bars indicating standard deviation. (c) The prevalence-based elimination feasibility coefficient, ε, for the PDD model (black bars) and the PDD-free model (red bars) across each round of MDA. Error bars represent standard deviation and the dashed line between years 7 and 8 indicates the timepoint at which ε becomes significantly (p<<0) negative.
Fig 5.
Correlation between mean ε and P(e).
Correlation between mean ε and P(e) for each parameter set derived from 1,000 simulations of the stochastic model. The model-free elimination feasibility coefficient is a strong predictor of the model-predicted probability of extinction even in the presence of demographic stochasticity and observation noise (R2 = 0.94; probit-transformed P(e)).
Fig 6.
Elimination feasibility coefficient sensitivity.
Sensitivity analysis showing how the elimination feasibility coefficient (ε) changes across transmission intensity, λ, and degree of PDD, κ. The surface shows a positive relationship between λ and ε and a negative relationship between κ and ε. At low transmission intensities, ε remains negative as long as κ ≠ 0 whereas high transmission intensities mostly eliminate the influence of PDD on ε, implying that annual MDA is insufficient to successfully interrupt transmission.