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 \( \begin{array}{cccccc}\hfill \downarrow {S}_0\hfill & \hfill \hfill & \hfill \downarrow {S}_1\hfill & \hfill \hfill & \hfill \hfill & \hfill \downarrow {S}_n\hfill \\ {}\hfill {h}_0(t)\hfill & \hfill \underset{\gamma_1}{\overset{\lambda }{\rightleftharpoons }}\hfill & \hfill {h}_1(t)\hfill & \hfill \underset{\gamma_2}{\overset{\lambda }{\rightleftharpoons }}\dots \hfill & \hfill \underset{\gamma_n}{\overset{\lambda }{\rightleftharpoons }}\hfill & \hfill {h}_n(t)\hfill \\ {}\hfill \downarrow \mu \hfill & \hfill \hfill & \hfill \downarrow \mu \hfill & \hfill \hfill & \hfill \hfill & \hfill \downarrow \mu \hfill \end{array} \)
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 |