Table 1 Parameter symbols and definitions

Previous formulations to predict impact based on of biological coverage of all blood resources

A

Availability of all blood hosts for attack, expressed as the rate at which they are collectively encountered and attacked per host-seeking mosquito per night[11, 24–30]

A _h,p

Availability of all protected (p) human (h) blood hosts for attack, expressed as the rate at which they are collectively encountered and attacked while protected by an LLIN or other prevention measure per host-seeking mosquito per night[11, 24–30]

C _A,p

Proportional coverage of all available blood resources that mosquito population utilizes (A) with a protective intervention (p)[11]

Reformulation to predict impact based on coverage and utilization rates of resource subsets

α _R

Utilization rate for an entire given resource (R, which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use), defined as the rate at which individual mosquitoes attempt to utilize all forms of that resource per gonotrophic cycle

${{\alpha }_R}_{{}_x}$

Utilization rate for a defined subset of a given resource (R, which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use) that can be identified and targeted with an intervention (x) in the field (R _x ), defined as the rate at which individual mosquitoes attempt to utilize the subset per gonotrophic cycle

${{\alpha }_R}_{{}_{x,y}}$

Utilization rate for a defined subset (x) of a given resource (R, which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use) that can be identified and targeted with an intervention (x) in the field during the subset of times (y) when it can be effectively protected by a given intervention (R _x,y ), defined as the rate at which individual mosquitoes attempt to utilize that subset at times when it can be protected per gonotrophic cycle

${{\alpha }_R}_{{}_{x,y,c}}$

Utilization rate for a defined subset of a given resource (R, which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use) that has been identified, targeted (x) and covered (c) with an intervention during the subset of times (y) when it can be effectively protected by a given intervention (R _x,y,c ), defined as the rate at which individual mosquitoes attempt to utilize that covered subset at times and places at which it can be protected per gonotrophic cycle

${{\alpha }_R}_{{}_{x,z}}$

Utilization rates for a defined subset of a given resource (R, which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use) that has been identified, can be targeted with an intervention (x) and has been surveyed entomologically (z) in the field (R _x,z ), defined as the rate at which individual mosquitoes attempt to utilize that sample of that subset per gonotrophic cycle

α _v

Utilization rate for all available blood resources (v), defined as the rate at which individual mosquitoes attempt to utilize any source of blood per gonotrophic cycle

${{\alpha }_v}_{{}_{x,z}}$

Utilization rate for a defined subset (x) of all blood resources (v) that has been identified and surveyed entomologically (z) in the field (v _x,z ), defined as the rate at which individual mosquitoes attempt to utilize that sample of that blood source subset per gonotrophic cycle

b

Mean lifetime total number of bloodmeals acquired per emerging mosquito[26]

B _l

Mean mosquito biting rates experienced by individual livestock (l), defined as the number of bites per head per night

B _h

Mean mosquito biting rates experienced by individual humans (h), defined as the number of bites per person per night[26, 30]

C _R

Coverage of all available forms of a given resource (R) with a vector control intervention

$C_{R_x}$

Coverage of all available forms of an identifiable, targetable subset (x) of a given resource (R) with a vector control intervention

$C_{v_{h,i,n}}$

Coverage of the human subset (x = h) of all available blood sources (v) while they are indoors (i) with long-lasting insecticidal nets (n)[11, 26–30]

E

Emergence or recruitment rate of mosquitoes in a defined setting per night[24, 26–29, 31]

h

Humans

i

Indoors

j

Gonotrophic age, expressed as the number of gonotrophic cycles completed

l

Livestock

λ _t

Relative availability of an individual mosquito traps (t) for attack by host-seeking mosquitoes attempting to utilize it as a source of blood, compared to a single unprotected human[27]

M

Absolute size of the mosquito population in a given setting, defined in terms of the number of individuals present

$m_{R_{x,z}}$

Rate at which the mosquito population utilizes a defined, entomologically surveyed sample subset (z) of any identifiable and targetable subset (x) of a given resource (R _x,z ), expressed as the number of utilization attempt events per night

$m_{v_{h,z}}$

Rate at which the mosquito population utilizes a defined, entomologically surveyed sample (z) of human (h) blood resources (v _h,z ), expressed as the number of utilization attempt events per night

$m_{v_{l,z}}$

Rate at which the mosquito population utilizes a defined, entomologically surveyed sample (z) of livestock (l) blood resources (v _l,z ), expressed as the number of utilization attempt events per night.

${\mu }_{R_c}$

Mortality probability associated with exposure to an intervention-covered (c) form of a given resource (R) through a single utilization attempt event

N _l

Number of livestock (l) living in a defined setting[24, 25, 27–29]

N _h

Number of humans (h) living in a defined setting[24, 25, 27–29]

N _h,z

Number of persons directly sampled by an entomological survey (z) of mosquitoes attacking human (h) hosts

N _h,Ω

Number of persons residing in all houses sampled by an entomological survey (Ω) of mosquitoes attacking human (h) hosts

N _t

Number of mosquito traps (t) present in a defined setting[27]

$P_{{\alpha }_{R_c}}$

Probability of a mosquito surviving all attempts to utilize intervention-covered forms of the targeted resource per gonotrophic cycle

P _γ

Probability of a mosquito surviving all utilization attempt events for all resources per gonotrophic cycle[24, 26, 28]

P _γ,0

Probability of a mosquito surviving all utilization attempt events for all resources per gonotrophic cycle in the absence of any intervention

P _f

Probability of a mosquito surviving one full feeding cycle (f)[24, 26–29, 31]

${\pi }_{v_{h,i}}$

Proportion of human (h) blood (v) host exposure to mosquito bites that occurs indoors (i) in the absence of any protective intervention[11, 24, 26, 30, 32–38].

$Q_{v_c}$

Proportion of all available bloodmeals (v) that originate from a specific livestock (l) host species subset[25]

$Q_{v_h}$

Proportion of all available bloodmeals (v) that originate from the human (h) host species subset[11, 22–27, 30, 39–41]

R

The total availability of all forms of a given resource, which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use, defined as the per night rate at which individual mosquitoes encounter and attempt to utilize that resource

R _x

The total availability of a subset (x) of a given resource (R which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use) that can be identified and targeted with an intervention, defined as the per night rate at which individual mosquitoes encounter and attempt to utilize that subset

R _x,y

The total availability of a subset (x) of given resource (R which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use) that can be identified and targeted with an intervention during the subset of times (y) when it can be effectively protected by that intervention, defined as the per night rate at which individual mosquitoes encounter and attempt to utilize that subset at times when it can be effectively covered with that intervention

R _x,y,c

The total availability of all intervention-covered (c) forms of a targetable subset (x) of given resource (R which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use) during the subset of times (y) when it can be effectively protected by that intervention, defined as the per night rate at which individual mosquitoes encounter and attempt to utilize the covered forms of that subset at times when it is effectively covered with that intervention.

R _x,z

The total availability of an entomologically surveyed sample (z) of a targetable subset (x) of given resource (R which may be specified as blood (v), resting sites (r), sugar (s) or any other resource mosquitoes use), defined as the per night rate at which individual mosquitoes encounter and attempt to utilize it.

r

The total availability of all forms of resting sites, defined as the rate at which individual mosquitoes encounter and attempt to utilize resting sites per night

s

The total availability of all forms of sugar, defined as the rate at which individual mosquitoes encounter and attempt to utilize sugar per night

t

Mosquito traps

τ

Mean number of nights individual mosquitoes spend resting and gestating indoors following a bloodmeal inside a house

v

The total availability of all forms of blood, defined as the rate at which individual mosquitoes encounter and attempt to utilize blood per night

x

A subset of a given resource that may be identified and targeted with a vector control intervention

y

A subset of a given resource that may be effectively covered with a vector control intervention at times and places when mosquitoes encounter and attempt to utilize it

z

A sample of a given resource that has been surveyed entomologically

Ω

Humans in a sampled set of households