Table 1 Variables and parameters for the feeding cycle model

Time, measured in whole units equal to average length of sporogonic cycle, from infection of mosquito by malaria to cycle from which mosquito gives infectious bites

D

input 0< D

Number of age classes included in analysis

λ

Cycle number (identifies specific cycle in the λ cycles over which probabilities are tracked in the FCM)

i

0≤ i ≤λ

Malaria status, the number of whole or partial cycles since infection with malaria

m

0≤ m ≤λ, m = 0 means not infected

Biopesticide infection status, the number of whole or partial cycles since infection with biopesticide

l

0≤ l≤ λ, l = 0 means not infected

Average number of eggs laid in cycle i by mosquitoes surviving to the start of cycle i

F _i

Average lifetime number of eggs laid per mosquito

φ

Average number of eggs laid in cycle i, by mosquitoes starting cycle i with malaria status m and biopesticide status l

f _i,m,l

m<i l<i

Average probability of survival from start of cycle i to start of cycle i+1

S _i

Average probability that a mosquito starting cycle i with malaria status m and biopesticide status l, will survive to start of cycle i+1

s _i,m,l

m<i l<i

Average probability of a mosquito being alive at start of cycle i.

V _i

Average probability of a mosquito being alive, with malaria status m and biopesticide status l, at start of period i.

v _i,m,l

m<i l<i

Probability that a mosquito alive at start of cycle i with malaria status m and biopesticide status l, survives and bites host type h in cycle i

q _i,m,l,h

m<i l<i

Type of host attacked

h

h=1, non-human

h=2, non-infectious human

h=3, infectious human

Average number of infectious bites in cycle i per mosquito alive at the start of cycle i

I _i

Average lifetime number of infectious bites per mosquito

u