Table 2.

SWB system

Host population H = ∑n  k = 0 h k is divided into burden strata {h k} by their worm load (w = # adult worms): k Δw ≤ w < (k + 1)Δw for h k. The partition is determined by worm-step Δw ≥ 1, that serves as hypothetical mating threshold. So h 0 are infection-free (no mated couples), while for h k (k ≥ 1) its mated count (expected number of couples) given by function (Eq. 1). The transitions among strata $\begin{array}{cccccc}\hfill \downarrow S_0\hfill & \hfill \hfill & \hfill \downarrow S_1\hfill & \hfill \hfill & \hfill \hfill & \hfill \downarrow S_n\hfill \\ \hfill h_0\left(t\right)\hfill & \hfill \underset{{\gamma }_1}{\overset{\lambda }{\rightleftharpoons }}\hfill & \hfill h_1\left(t\right)\hfill & \hfill \underset{{\gamma }_2}{\overset{\lambda }{\rightleftharpoons }}\dots \hfill & \hfill \underset{{\gamma }_n}{\overset{\lambda }{\rightleftharpoons }}\hfill & \hfill h_n\left(t\right)\hfill \\ \hfill \downarrow \mu \hfill & \hfill \hfill & \hfill \downarrow \mu \hfill & \hfill \hfill & \hfill \hfill & \hfill \downarrow \mu \hfill \end{array}$ are determined by force of infection (FOI) λ (= rate of worm accumulation/Δw), resolution rates γ k = k γ (γ - mean worm mortality), and population turnover rate μ (mortality, maturation, migration, etc.). Source terms S k represent demographic inputs from related population groups, e.g. for children S 0 = b H (birth rate), with S k ≥ 1 = 0 (as all newborns are infection-free); whereas adult sources come from maturing child strata. For the interested reader, a version of the SWB model programmed in Mathematica software is provided as Additional file 1