Eliminating malaria requires vector control interventions that dramatically reduce adult mosquito population densities and survival rates. Indoor applications of insecticidal nets and sprays are effective against an important minority of mosquito species that rely heavily upon human blood and habitations for survival. However, complementary approaches are needed to tackle a broader diversity of less human-specialized vectors by killing them at other resource targets.

Impacts of strategies that target insecticides to humans or animals can be rationalized in terms of

The usefulness of this approach is illustrated by deriving utilization rate estimates for various blood, resting site, and sugar resource subsets from existing entomological survey data. Reported impacts of insecticidal nets upon human-feeding vectors, and insecticide-treated livestock upon animal-feeding vectors, are approximately consistent with model predictions based on measured utilization rates for those human and animal blood resource subsets. Utilization rates for artificial sugar baits compare well with blood resources, and are consistent with observed impact when insecticide is added. While existing data was used to indirectly measure utilization rates for a variety of resting site subsets, by comparison with measured rates of blood resource utilization in the same settings, current techniques for capturing resting mosquitoes underestimate this quantity, and reliance upon complex models with numerous input parameters may limit the applicability of this approach.

While blood and sugar consumption can be readily quantified using existing methods for detecting natural markers or artificial tracers, improved techniques for labelling mosquitoes, or other arthropod pathogen vectors, will be required to assess vector control measures which target them when they utilize non-nutritional resources such as resting, oviposition, and mating sites.

The online version of this article (doi:10.1186/1475-2875-13-338) contains supplementary material, which is available to authorized users.

While antiparasitic drugs and vaccines will be essential to the final stages of malaria elimination, their effectiveness as transmission control interventions will rely heavily upon unprecedented levels of vector control in highly endemic settings
[

Faced with such an array of resource target options, the challenge is to define exactly which of these intervention targets are optimal in each of the diverse vectorial systems that exist
[

All symbols used are listed and defined in Table

Symbol | Definition |
---|---|

| |

| 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
[ |

_{h,p}
| Availability of all protected ( |

_{A,p}
| Proportional coverage of all available blood resources that mosquito population utilizes ( |

| |

_{R}
| Utilization rate for an entire given resource ( |

| Utilization rate for a defined subset of a given resource (_{x}), defined as the rate at which individual mosquitoes attempt to utilize the subset per gonotrophic cycle |

| Utilization rate for a defined subset (_{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 |

| Utilization rate for a defined subset of a given resource (_{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 |

| Utilization rates for a defined subset of a given resource (_{x,z}), defined as the rate at which individual mosquitoes attempt to utilize that sample of that subset per gonotrophic cycle |

_{v}
| Utilization rate for all available blood resources ( |

| Utilization rate for a defined subset (_{x,z}), defined as the rate at which individual mosquitoes attempt to utilize that sample of that blood source subset per gonotrophic cycle |

| Mean lifetime total number of bloodmeals acquired per emerging mosquito
[ |

_{l}
| Mean mosquito biting rates experienced by individual livestock ( |

_{h}
| Mean mosquito biting rates experienced by individual humans ( |

_{R}
| Coverage of all available forms of a given resource ( |

| Coverage of all available forms of an identifiable, targetable subset ( |

| Coverage of the human subset ( |

| Emergence or recruitment rate of mosquitoes in a defined setting per night
[ |

| Humans |

| Indoors |

| Gonotrophic age, expressed as the number of gonotrophic cycles completed |

| Livestock |

_{t}
| Relative availability of an individual mosquito traps ( |

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

| Rate at which the mosquito population utilizes a defined, entomologically surveyed sample subset (_{x,z}), expressed as the number of utilization attempt events per night |

| Rate at which the mosquito population utilizes a defined, entomologically surveyed sample (_{h,z}), expressed as the number of utilization attempt events per night |

| Rate at which the mosquito population utilizes a defined, entomologically surveyed sample (_{l,z}), expressed as the number of utilization attempt events per night. |

| Mortality probability associated with exposure to an intervention-covered (c) form of a given resource ( |

_{l}
| Number of livestock ( |

_{h}
| Number of humans ( |

_{h,z}
| Number of persons directly sampled by an entomological survey ( |

_{h,Ω}
| Number of persons residing in all houses sampled by an entomological survey ( |

_{t}
| Number of mosquito traps ( |

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

_{γ}
| Probability of a mosquito surviving all utilization attempt events for all resources per gonotrophic cycle
[ |

_{γ,0}
| Probability of a mosquito surviving all utilization attempt events for all resources per gonotrophic cycle in the absence of any intervention |

_{f}
| Probability of a mosquito surviving one full feeding cycle ( |

| Proportion of human ( |

| Proportion of all available bloodmeals ( |

| Proportion of all available bloodmeals ( |

| The total availability of all forms of a given resource, which may be specified as blood ( |

_{x}
| The total availability of a subset ( |

_{x,y}
| The total availability of a subset ( |

_{x,y,c}
| The total availability of all intervention-covered ( |

_{x,z}
| The total availability of an entomologically surveyed sample ( |

| 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 |

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

| Mosquito traps |

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

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

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

| 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 |

| A sample of a given resource that has been surveyed entomologically |

| Humans in a sampled set of households |

Biological coverage (_{A,p}) of all the blood resources upon which mosquitoes rely, with long-lasting insecticidal nets (LLINs) or any other personal protection measure, has been previously defined as the proportion of all mosquito attacks upon all available hosts for which those hosts were covered with a protective (

where the total attack availabilities of the all hosts (_{p}), are defined kinetically
[

However, to allow simplified notation for generalization of this approach to a greater diversity of distinct resources, here the symbol

where _{v} is the proportion of all mosquito attacks upon real (live vertebrate hosts) or perceived (artificial odor-baited traps, sometimes referred to as pseudo-hosts
[_{c} is the total rate at which individual mosquitoes encounter and attack all hosts and pseudo hosts at times and places when they are effectively covered with a vector control intervention.

In the case of interventions such as LLINs, which only protect humans while they use them indoors, biological coverage can be calculated as the product of the proportion of all bloodmeals (

where all three terms on the right hand side of Equation

Expressing Equation

LLINs that directly kill mosquitoes when they encounter and attack protected human blood sources are the best established
[_{R}). This definition of resource utilization rate can be expressed mathematically as the product of the duration of the gonotrophic cycle, expressed as nights per gonotrophic cycle (_{R}), divided by the size of the mosquito population (

where _{R} in units of utilization attempt events per night, and _{c}), the corresponding rate at which mosquitoes encounter and attempt to utilize that covered fraction

Hence the quotient of the availability or utilization rates for the total resource, divided into those for the intervention-covered fraction, are equivalent to biological coverage of that resource:

Most vector control strategies only target a specific subset (_{x}) of that resource

Similarly, the proportion of that subset (

Hence, the biological coverage of all forms of that resource (_{R}) can be expressed more explicitly than in Equation

Note that

Interventions targeting adult mosquitoes may have quite complex modes of action, repelling mosquitoes away from humans
[_{v}=1). All predictions of impact upon mosquito survival, and the entomologic inoculation rates they mediate, were implemented and parameterized exactly as previously described
[

where _{γ} is the probability of surviving all utilization attempt events for all resources per gonotrophic cycle, _{γ,0} is the probability of surviving all utilization attempt events for all resources per gonotrophic cycle in the absence of any intervention, and

By substituting rearranged forms of Equation

It is therefore not necessary to know the proportion of that total resource which the targeted subset represents, or the coverage (_{R}) or utilization rate (_{R}) for all available forms of a resource. Impact can be predicted directly so long as the coverage of the targeted subset itself

This approach to predicting the survival probability assumes that utilization attempt events are randomly, and independently, distributed across all resource units and mosquitoes. Specifically, the number of times one mosquito utilizes a resource (or resource subset) in one gonotrophic cycle is assumed to be a non-negative integer valued random variable (0, 1, 2, 3…) since the mosquito may not necessarily use the resource or, alternatively, may access it multiple times. Hence, the utilization rate of these resources should be understood as an expected value depending on random events that may be expressed as a mean. This is clearly not the case in relation to obligate utilization of blood from one of _{R} = 1) that are utilized at a mean rate of once per gonotrophic cycle (_{R} = 1) with an insecticide which induces comprehensive fatality

Adult mosquitoes use many distinct resources during their lifetimes, including several that they need afresh every time they complete a gonotrophic cycle: blood, resting sites, and oviposition sites. Most of these resources are difficult to quantify directly, so the same is true of the rates at which mosquitoes utilize them, thereby making contact with them. However, measurements of feeding rates upon humans or livestock allow ready quantification of absolute mosquito population size or recruitment rate
[_{v} ≈ 1) where sugar availability is not limiting
[_{h}), the number of humans living there (_{h}), the proportion of bloodmeals obtained from humans
_{f})
[

where the mean lifetime number of bloodmeals per emerging mosquito (

Similarly, for a very zoophagic (predominantly animal-feeding) vector with a strong preference for a known, accessible, manageable non-human host species such as cattle, goats, sheep, pigs or other livestock (_{l}) so the equivalent calculation can be made if the proportion of blood obtained from that host species
_{l}) can be determined:

The key to applying Equations _{x,z}) if the proportion of all available forms of that resource which that surveyed subset represents (_{x,z}_{R}), are both known. Note also that equation _{v} ≈ 1) but can be explicitly reintroduced for the purposes of generalization. Substituting
_{h} or _{l}, _{x,z}_{R} for _{v} in Equations

Blood resources can be readily identified as discrete units and their total numbers can be quantified by head-count census. However, units of sugar, resting site, oviposition site, and mating site resources are difficult to define unambiguously, except where these are introduced artificially (sugar baits, houses, boxes, pots, barrier screens, water containers, or swarming markers), and the total quantity of these resources available in the environment is even more difficult, if not impossible, to ascertain. Therefore, it is not obvious how _{x,z}_{x,z}. Also, the per gonotrophic rates at which mosquitoes attempt to utilize (_{x}), as well as the per night rate at which utilization attempt events occur (_{x}), are distinguished from those for other resources with the specific terms
_{x}/_{x,z}), by an equivalent formulation specified for all blood resources, and a surveyed sample of hosts from a subset for which bloodmeals recovered from the midguts of recently fed specimens can be identified and distinguished from other sources (_{x,z}), and rearranging:

Note that the emergence and mean longevity terms cancel each other out so that estimates of these parameters are not required to estimate the relative rate of utilization of a resource compared with blood, as described below.

The most obvious vertebrate blood resource subsets (_{x}) which are readily surveyed, including detection of blood feeding events and identification of blood source in specimens of fed mosquitoes, are humans (_{h,z}) or cattle (_{l,z}) sampled by the host attack survey, divided by the total number of humans (_{h}) or livestock (_{l}) present:

Fortunately, while gonotrophic discordance beyond the first feeding cycle does occur in _{v} ≈ 1), so substituting the host-specified (_{x}
_{h} or _{l}) formula of Equation _{v} with unity, yields a solution for

or

where _{x,z}/_{x} is the proportion of all available forms of the targeted non-blood resource subset that was surveyed entomologically to measure the rate per night at which the entire mosquito population attempts to utilize it
_{h,z}/_{h} and _{l,z}/_{l} are the proportions of all humans or livestock that were respectively surveyed to measure the rate at which mosquitoes attempted to utilize their blood, and where

Where two resources co-occur and overlap completely with each other, specifically the example of resting sites (_{i}) and human blood indoors within houses (_{h,i}), the proportion of each resource subset that is sampled is no longer required because these cancel each other out. All that is required is an estimate of the number of persons or person nights sampled by the host attack survey (_{h,z}), and the total number people staying in those sampled houses (_{h,Ω}), or even their ratio, which is commonly referred to as the mean number of occupants per house (_{h,Ω}/_{h,z}):

In some experiments, however, resting events following more than one bloodmeal are represented in surveys of resting sites because those events may last two or more days. Recent standardized trials to compare various techniques for catching host-seeking and resting mosquitoes
[

Studies, or sets of studies, were identified which presented sufficient parameter estimate data for utilization rates of specific, intervention-targetable resource subsets to be calculated for specific malaria vector species in specific, distinct locations. In addition to the authors’ archives of literature and unpublished data, the Pubmed database was also queried with the search term ‘

Utilization rates for blood from humans while indoors, when they can be protected with LLINs, was calculated as the product of the proportion of human exposure to mosquito bites occurring indoors

Where local estimates for the proportion of bloodmeals obtained from humans

Utilization rates for odour-baited traps are calculated by assuming that the probability of a mosquito attacking a trap, rather than a natural host, per gonotrophic cycle is equivalent to the proportion of all available human hosts, animal hosts, and pseudo-hosts, that they represent
[_{t}_{h}), the relative availability of those traps (_{t}), and the proportion of bloodmeals obtained from non-human hosts

Utilization rates for sugar resource subsets

Utilization rates for resting site subsets
_{r,x,z}) adjusted, where necessary, for an assumed indoor resting period of 2 days (_{h,Ω}/_{h,z}) adjusted for reported usage rates of LLINs

Figure

Figure

Apart from blood, the other important nutrition source that facilitates mosquito survival and malaria transmission is plant-derived sugar
[

Utilization rate estimates for indoor resting sites (Figure

Estimating coverage and utilization of a resource subset primarily depends upon defining it in a quantifiable manner that can be readily surveyed and targeted, or artificially created in the field. The most obvious and familiar examples are the human populations targeted for universal coverage with LLINs to protect the blood resource they represent to mosquitoes
[

The subset of all resting sites represented by the inner surfaces of human dwellings (walls, ceilings and even furniture) are the defined target for IRS
[

Comparing the range of utilization rates described in Figure

Utilization rates for resting site subsets (Equation

Fortunately, a wide range of more sensitive chemical, biochemical, genetic and biological markers, that could be applied to labelling mosquitoes when they use these other resources, are now available
[

The conceptual framework and entomological measurement priorities outlined here should be readily and directly applicable to almost any population of mosquitoes, vectors or other pest. It should therefore be possible to simultaneously tackle multiple vectors with integrated vector management programmes
[

The concept of biological coverage can be extended to enable prediction of intervention impact for diverse vector control strategies based on estimated utilization rates for any definable, targetable resource subset. Indeed the applicability of this approach has been demonstrated here using existing entomological measurement methods to rationalize the observed impacts of LLINs, insecticide-treated livestock, and attractive toxic sugar baits upon malaria vectors. The development of improved and diversified technologies for controlling transmission of malaria, as well as a diversity of other vector-borne pathogens, could therefore be accelerated, rationalized and streamlined based on field measurements of the rates at which mosquitoes utilize targetable biological resource subsets.

While blood and sugar consumption can be readily quantified using existing methods for detecting natural markers or artificial tracers, improved techniques for labelling mosquitoes will be required to assess and optimize vector control measures which target them when they utilize resting, oviposition and mating sites. All mosquito species need sugar, resting sites, oviposition sites, and mating sites, as indeed do most arthropods of medical and veterinary importance. These resources are therefore important potential targets for the new or improved vector control methods that are clearly needed to eliminate malaria, and also a variety of other vector-borne pathogens. To enable comparative assessment of all potential resource subset targets, including sites which mosquitoes rest, oviposit or mate at, existing tracer technologies need be adapted to enable reliable, non-toxic, non-disruptive labelling of mosquitoes when they utilize these non-nutritional resource subset targets.

Additional file 1:

The authors declare that they have no competing interests.

GFK, AS, JEG, JS, and CJD developed the study hypotheses, contributed data for the analysis, and assisted in the revising the manuscript. GFK conceived the study, developed and applied the model and drafted the manuscript in consultation with the other authors. NC, SSK, and GC refined the mathematical formulation of the model. NC oversaw finalization of the manuscript. All authors read and approved the final manuscript.

We thank Dr. K Aultman and Dr. D Malone for discussions that stimulated and influenced the content of this manuscript. We thank Prof T A Smith for guidance on the probablistic basis of exponential decay models, and Dr. T R Burkot for critical comments on the manuscript, as well as providing population size data for Haleta. We are also grateful to three anonymous reviewers, whose comments had a substantive influence on the final interpretation and conclusions. This work was funded by the Bill & Melinda Gates Foundation (Award numbers 45114, 52644 and OPP1032350).