MWB |
Mean Worm Burden |
SWB |
Stratified worm burden |
NB |
Negative binomial (distribution) |
MDA |
Mass drug administration |
FOI |
Force of infection |
BRN or |
Basic reproduction number in MacDonald MWB system |
|
critical BRN-type parameter for breakpoint in MWB system |
H
|
Total host population |
|
n-th human strata in SWB system (population fraction carrying n worms) |
|
Demographic sources for nth strata in SWB system |
|
Worm increment in SWB formulation |
w
|
Worm burden (MWB), −1st moment of SWB system |
u
|
2nd moment of SWB system: |
W
|
Total worm population ( = H w) |
U
|
Total 2nd moment ( = H u) |
|
Source terms in the w- and u- equations |
k
|
NB (negative binomial) aggregation parameter |
|
Human population turnover rate (.02−.05/year) |
|
Worm mortality rate ( = 1/4 years) |
|
Snail mortality ( = 5/year) |
|
Human FOI ( = mean rate of adult worm accumulation in human hosts) |
|
Snail FOI (transition rate “susceptible” −> “infected”) |
|
Mated female number for mixed strata (i males and j females) |
|
Mated female count for n-th strata made of n adult worms |
|
Total mated female count in host population |
|
Mating function in MacDonald (MWB) system with NB worm distribution |
|
Allee mating hurdle factor () |
A
|
Transmission rates (snail->human) per single infected snail |
B
|
Transmission rates (human->snail) per mated female |
|
Relative transmission rates |
|
Infectious prevalence in MWB system with mean w, and NB aggregation k
|
|
Infectious prevalence in SWB system with FOI , and host turnover |
|
Reduced “snail equilibrium” function for MWB (MacDonald) system |
|
Reduced “snail equilibrium” function for SWB system |
|
Drug efficacy (fraction of worms surviving a single dose) |
f
|
Population fraction cover in MDA |
E
|
Mean egg count in host population |
|
Egg production/mated female |
|
Equilibrium levels for MWB, SWB systems |