Table 4.
Dynamic variables for the snail model are population densities (per unit habitat) x: susceptible; y: prepatent; z: patent; N = x + y + z- total. Basic processes and parameters include (i) snail reproduction (logistic growth) β = β 0(x + y)(1 − N/K), with maximal reproduction rate β 0 and carrying capacity K; (ii) snail mortality v; (iii) snail FOI Λ(determined by human host egg outputs) ; (iv) recovery rate r (prepatency period 1/r) (v) patency conversion fraction c. In population growth term β, only susceptible and prepatent snails (x + y) reproduce. Combined growth-SEI dynamics consists of 3 differential equations Parameter values and ranges for the snail system are given in Table 5. Short-lived larval stages (M, C) equilibrate rapidly at levels proportion to human/snail (H, N) multiplied by their respective infectivity. Specifically, C* = α C N z; M* = β M ω H E (6) where (“C-production /patent snail” over “C-mortality”). For miracidia the relevant inputs include environmental egg-release by host population ω H E, ω = human-snail contact rate, H - population size, E - mean host infectivity - egg release (Eq. 5), coefficient (“survival fraction of eggs” over “M - mortality”) |