Description of the model

This is an adaptation of a deterministic model representing the most important host-seeking, survival and malaria transmission processes that individual mosquitoes undertake before they can transmit malaria [43]. All parameter symbols and their meanings are outlined in tables 1 and 2. Versions of the original model have been used to explore effects of bednets, cattle, repellents and insecticides on malaria transmission [44], to outline global coverage targets [36] and likely efficacy of ITNs [45], and also to examine interactions within push-pull strategies such as combining net-use with zooprophylaxis using cattle [46].

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Table 1. Symbols and their meanings.

https://doi.org/10.1371/journal.pone.0011573.t001

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Table 2. Symbols and their meanings-continued from table 1.

https://doi.org/10.1371/journal.pone.0011573.t002

Blood feeding is the most important epidemiological event in the interactions between humans and malaria vector mosquitoes [47], [48]. In this model, the blood acquisition process is considered as having three phases: 1) the mosquito being in a host-seeking state, 2) the mosquito attacking the host (or diverting away) and 3) the mosquito feeding upon the host (Fig. 1). As in previous works by other authors, this feeding process is considered to be cyclical rather than continuous, so as to more accurately represent natural events [49], [50]–[52]. The model examines diversion and mortality processes that occur during the three phases and how changes induced by interventions upon these processes can contribute to individual and community-level protection against malaria.

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Figure 1. A simplified conceptual structure of the adapted model.

This figure shows behavioral and mortality processes that occur in a mosquito feeding cycle. The host-seeking process includes non-host oriented kinesis and host-oriented taxis. The gray circular area represents extent of detectable odor plume around a host of species or type (s). In blood acquisition processes, mosquitoes are said to encounter hosts when they first detect odor cues associated with that host (ε_s). Then they can either attack the encountered host (γ_s) or be diverted back to non-host-oriented kinesis (Δ_s). Mosquitoes which go on to attack the host can either successfully feed (φ_s) or die (μ_s). Mosquitoes which successfully feed will go on to rest, digest the blood meals and then oviposit their eggs before eventually returning to host seeking state. This diagram is not drawn to scale and the host odor plume may not always be circular.

https://doi.org/10.1371/journal.pone.0011573.g001

Effects of odor-baited traps were simulated in conceptual environments of two alternative dominant vector species (Anopheles gambiae sensu stricto Giles or An. arabiensis Patton) [53] in the presence of cattle, the main alternative blood source for these vectors [54], and presence or absence of ITNs. In each test scenario, the technology was evaluated in terms of combined, individual and community-level protection against malaria transmission when traps are implemented alone or in combination with ITNs.

Similar to most malaria transmission models, an enclosed ecosystem of parasites, vectors and hosts, is assumed [55], [56]. In order to further reduce computational complexity, the human hosts are considered to be homogenously mixed, meaning that vulnerability of individuals to malaria infection [5], [57] or attractiveness of individuals to mosquitoes [2], [58], [59] can be reasonably estimated using population mean values for these parameters. These assumptions allowed for exploration of what might be possible if the traps are concentrated in geographical areas where mosquito densities are most abundant. Such locations are known to exist in real field settings [60]–[62] and can be targeted to achieve greatly enhanced control of pathogen transmission [63].

In the original model, the term ‘hosts’ referred to any vertebrate blood-sources upon which vectors can feed. This definition is hereby expanded to include all entities that a vector can attack with the intention of taking a blood meal, regardless of whether that entity actually has blood or not. This redefinition allows for inclusion of odor-baited traps as additional hosts (more precisely, pseudo-hosts) even though mosquitoes cannot possibly obtain blood from them. Another modification was a more explicit sub-division of the host-seeking process. Unlike the original model, the host-seeking process is considered here as consisting of two successive stages leading to the mosquito attacking the host namely: 1) non-host oriented kinesis, referring to arbitrary movements of the mosquito before it detects host cues, a process which ends with a host encounter event, and 2) host-oriented taxis, referring to directional movements of the mosquito once it encounters and detects the host cues in the environment and starts moving towards the source of those cues, a process which if initiated, either ends with a host attack event, or is aborted resulting in diversion back to kinesis (Fig. 1).

The duration of non-host-oriented kinesis, which is equivalent to the reciprocal of the rate at which an individual host is encountered by an individual vector, depends on: 1) physical distance between hosts and mosquitoes and 2) the distance over which attractive host odor plumes can extend. This means mosquitoes are more likely to encounter hosts which are near to the point at which they began host-seeking than those hosts which are far away. In nature, such spatial relations, including modifiers such as topography and wind direction are known to be important determinants of rates at which individual hosts are encountered [60]–[65]. This definition of the kinesis process also means that mosquitoes will more readily encounter hosts whose odor plumes extend over a wide radius than hosts which have short-radius plumes. For the purposes of this model, wider odor plumes are regarded as being equivalent to more mosquitoes potentially falling within the range of host encounter. Therefore hosts generating such kairomonal plumes are considerably more readily available than hosts generating less dispersed, short radius plumes. Interestingly, recent field trials of odor-baited traps demonstrate that the host-specific cues which malaria vector mosquitoes use to identify their preferred human hosts act mainly as long range attractants, presumably triggering the encounter process itself and allowing mosquitoes to make the choice between attack and diversion as early and as efficiently as possible [41].

Host-oriented taxis begins immediately after host encounter once the mosquito as chosen to proceed with host attack. There is a possibility that a mosquito encountering a non-preferred host type will ignore the opportunity to approach the host or may discontinue taxis, thus diverting back to non-host-oriented kinesis to seek other hosts. Once the mosquito commits to attack a host, it is assumed to complete a full taxis phase which ends with the host attack event.

The original definition of host availability [43] was also altered to specifically and separately describe the availability of hosts for attack rather than availability of host blood per se. The availability (a) of any host of any species or type (s) for mosquitoes to attack is the product of the rate at which individual vectors encounter that host (ε_s) and the probability that, after this encounter, they will attack the host (γ_s):(1)Previously, host availability had been described as the product of host encounter rate and feeding probability [43], [44], [46], [54]. Replacing the term, feeding with the term, attack, allows us to model the behavior of mosquitoes which attack the odor-baited traps and for which the feeding probabilities are therefore nil. A closer examination of what was previously defined as host availability [43] reveals that actually, it represents the availability of host blood at a particular source rather than the availability of the hosts themselves. That is to say, the availability of host blood (z) from a host of any species or type (s) is the product of the rate at which individual vectors encounter this host (ε_s) and the probability that, after this encounter, they will successfully feed upon that particular host (φ_s):(2)

Similar to the original model, we label certain parameters with subscript s to represent different host species or host types including humans, cattle or odor-baited traps. Also, where necessary, the subscript s is specified as one of three different subscripts, t, c, h to represent traps, cattle and humans respectively. Moreover, humans not using nets (unprotected humans) and humans using nets (protected humans) are in some cases specifically represented by subscripts h,u and h,p respectively. Another subscript, j, which was used in previous versions of the original model [43], [44] to represent individuals within different host types or species, has been omitted in this reformulation, as no specific individual hosts are considered and instead, all parameters in this paper represent mean values for respective host populations.

When the mosquito encounters the host, it can either attack the host (successfully completing the host-seeking process, but not necessarily the blood acquisition process) or it can be diverted from the host (aborting the host-seeking process). The attack (γ_s) and diversion (Δ_s) probabilities therefore sum to unity.(3)

After host encounter, all diverted mosquitoes are assumed to re-enter non-host-oriented kinesis afresh. The diversion may include behavioral responses of mosquitoes to non-preferred or protected hosts which prompt them to abort taxis. For preferred hosts, diversion may be induced by physical barriers like house screens and untreated nets or chemicals used to treat nets or houses, and which repel or irritate mosquitoes [66], [67].

However, not all vectors that attack the host will successfully feed. To account for mosquitoes that die during this attack process, a term for the mean attack-related mortality (μ_s) is introduced. It is assumed that only two possibilities exist at this stage: either the vector feeds successfully and consequently survives or it dies in the attempt before obtaining a blood meal. All mortality risks associated with host attack are expressed as a single mean probability and assumed to occur prior to feeding. The probability of successful feeding per host encounter (φ_s) is therefore calculated as follows:(4)Assuming similar levels of baseline host defensiveness, the probabilities of diversion (Δ) and attack related mortality (μ) are considered to be same for cattle (c) and humans who are not using ITNs, i.e. unprotected humans (h,u). Equation 4 can therefore be specified as follows:(5)

Personal and house-hold protection measures such as bednets, repellents or domestic insecticides function by diverting host-seeking vectors or killing the vectors. The terms, Δ and μ are therefore modified for ITN users i.e. protected humans (h,p), to become Δ_h,p and μ_h,p respectively. Consistent with Killeen & Smith (2007) [44], the new terms are obtained by adding the ITN-induced changes to the baseline diversion and baseline mortality values:(6)(7)Where, θ_Δ and θ_μ represent the additional effects of ITNs on the diversion and mortality probabilities respectively. These coefficients were previously annotated as Δ_p and μ_p in the original model [43], [44] but have now been changed to distinguish them more clearly from the Δ_h,p and Δ_h,u, which refer to diversions from protected and unprotected humans respectively. The term π_i in the two equations refers to the proportion of normal exposure to mosquito bites upon humans lacking ITNs that occurs during the times when nets would normally be in use [45], [68]. It is used here to modify the terms θ_Δ and θ_μ, in order to obtain the true effects of ITNs upon a typical user. Without the term, π_i, the equations would represent merely an ideal situation where ITNs are consistently and correctly used over the full course of the time when malaria vectors bite. However, such an ideal scenario seldom happens and possessing a net does not always translate to consistent and perfect use of it. Moreover, even the most nocturnal vectors can feed to some extent in the early evening hours before people go under their nets or in early mornings when many people are awake and are no longer protected [45], [67], [68]. Thus in practice, not all human exposure to mosquito bites occurs during the times when nets are actually in use [45], [67]–[69]. Note that this approach deals more simply and parsimoniously with such behavioral avoidance of interventions, than previous approaches by incorporating these effects at the single point of the model where they actually act in biological reality, rendering the more elaborate and indirect formulations such as equation 8 in Killeen et al., 2007 [43] and equation 1 in Govella et al., 2010 [45], redundant.

Equations 6 and 7 are used to specify equation 4 in order to explicitly express the probability of successful feeding upon an ITN user (φ_h,p):(8)

Modeling the effects of individual odor-baited traps

Odor-baited traps are assumed to affect the foraging behavior of host-seeking mosquitoes by triggering the transition from kinesis to taxis, in exactly the same way as vertebrate hosts. Their efficacy as tools to control malaria transmission is derived primarily from two complementary characteristics: 1) their high attractiveness to malaria mosquitoes compared to attractiveness of humans [41] and 2) their ability to trap and kill mosquitoes which attack them thus removing these mosquitoes from the biting population. Any given trap type can therefore be described in terms of its mean availability for attack by host-seeking mosquitoes (a_t), defined as the rate at which it is encountered (ε_t), and the probability that it is attacked by the mosquitoes (γ_t) following encounter. As successful blood feeding upon a trap is not a possible outcome, the mortality probability for mosquitoes that attack a trap (μ_t) and the corresponding probability of successful blood feeding (φ_t), are fixed at one and zero respectively (μ_t = 1, φ_t = 0).

These assumptions about individual-level processes enable adaptation of subsequent equations from the original formulation [43], so as to estimate population-level effects of odor-baited traps used alone or in combination with ITNs, and also to elucidate desirable characteristics of such devices.

Estimating population level effects of odor-baited traps when used alone or in combination with ITNs

The availabilities of cattle (a_c) and traps (a_t) for attack by host-seeking mosquitoes were calculated based on field estimates of their relative availabilities (λ_c for cattle [54] and λ_t for odor-baited traps [41]) when compared to the availability of humans for similar attacks as described in equation 1:(9)(10)

For any given number of odor-baited traps (N_t), cattle (N_c), people not using ITNs (N_h,u) and people using ITNs (N_h,p), the total host availability (A) was calculated as the sum of the products of mean availabilities of each host species or type (a_s) and the number of hosts of that particular species or type (N_s). However, unlike in the original formulation [43], the term host availability hereby includes events only up to host attack, thus excluding all probabilities of blood feeding or death after the attack. The mean host-seeking interval (η_v) was then calculated as the reciprocal of total host availability (A) and consistent with previous formulations [54]:(11)

The relative exposure of any host to mosquito bites (which is calculated as a function of successful feeding and therefore the availability of blood rather than hosts per se) is therefore no longer equivalent to its relative availability when calculated as a function of host attack probability. This means that any two hosts can be equally available for attack but may be differentially exposed if interventions which cause different levels of reduction of successful feeding despite equal levels of diversion are specified. The relative exposure (ψ) of different hosts must therefore be calculated separately from relative availability of attackable hosts and must be based on the availability of the blood resource that each host type or species (s) represents to mosquitoes (z_s). For example, relative exposure of humans protected with ITNs, when compared to that of humans not protected with ITNs is calculated as follows:(12)where z_h,p refers to the mean availability of blood from a protected human.

For a vector to complete one feeding cycle, it must survive all the host-seeking phases shown in figure 1 including gestation to convert blood to eggs and then an equivalent set of resource acquisition processes required to enable oviposition. While gestation is primarily spent resting in relatively safe places, which are often inside houses, foraging for resources is an intrinsically dangerous process for mosquitoes. Even without any human intervention, survival is reduced by numerous biotic and abiotic factors in the environment such as predators, host defensive behavior and dehydrating conditions of heat and low humidity [70], [71].

As in our original model [43] and in some previous models by other authors [50], [72], it was assumed that survival during host-seeking and oviposition site-seeking phases is lower than survival while the mosquito is resting inside houses. Survival across all phases of the gonotrophic cycle was estimated as the distinct daily survival probability during each phase to the power of the respective time intervals, namely the host-seeking interval (η_v), gestation interval (g) and oviposition site-seeking interval (η_o). Though the current definition for host-seeking refers to processes up to and including attack, but not blood acquisition itself, the duration between the time when the mosquito attacks the host and the time when it bites and acquires blood from it, is considered here to be a negligible interval in the context of a gonotrophic cycle which lasts for two or more days. The daily survival probability of a resting mosquito is defined as P and the survival probabilities during host-seeking and oviposition site-seeking are assumed to be equal and are both defined using the term (P_ov). The survival rate per feeding cycle (P_f) was therefore estimated as the combined probability that a vector survives gestation (P^g), oviposition site-seeking (P_ov^ηo), host-seeking (P_ov^ηv) and the eventual attack of a host (P_γ):(13)

To calculate the probability of mosquitoes surviving their eventual attack upon any host (P_γ), we assumed that the proportion of all attacks that end in death is the mean of the mortality probabilities for attacking the various hosts (non-ITN users, ITN users, cattle or odor-baited traps), weighted according to the proportion of total availability that each host class represents [45]:(14)

This term differs slightly from equation 13 of the original formulation [43], in that it now reflects ITN effects that have been modified by the proportion of normal unprotected human exposure that occurs during times when this intervention would typically be in use (π_i) [45], [68], but does so more directly than the more complex formula of Govella et al., 2010 [45] because this effect has already been captured by equations 6 and 7. The term for mortality upon attacking an odor-baited trap (μ_t) could be included explicitly in the numerator so that the equation is clearer, but because it has already been defined as being equal to one, the trap terms in both the numerator and denominator are expressed simply as a_tN_t. Here again, this revised formulation is more specific and predicts survival of attack based only on rates of attack rather than the probabilities of successful feeding.

The human blood index (proportion of all blood-meals that originate from humans; Q_h), was calculated based on the proportion of the total availability of blood from all host types (Z), which humans represent (Z_h). Note that for any host species or type, Z_s = z_sN_s. Specifically, Q_h was therefore calculated as the proportion of surviving mosquitoes obtaining a blood meal that do so from humans, based upon the overall total rates of encounter of each host type and the probabilities of successfully obtaining a blood meal from each:(15)(16)(17)It should be noted that equation 17 also does not contain terms for odor-baited traps (N_t, ε_t and φ_t) in the denominator. This is because it is impossible for mosquitoes to obtain blood meals from the traps so even if the term φ_t were included, it would be valued zero thus rendering the equation mathematically equivalent to the above.

Estimating protection against exposure to malaria

As described in the very first formulation of the population-level component of this hierarchical model [73] and its subsequent improvements [43], [44], the survival rate per feeding cycle (P_f) and the proportion of blood meals taken from humans (Q_h) were used to calculate the potential of any individual vector to transmit malaria from infectious humans over its lifetime (L). The term L together with human infectiousness to mosquitoes (κ) were then used to calculate the mean number of infectious bites per emerging mosquito during its lifetime (β). To obtain the sum of all infectious bites that occur in the whole human population, the mean number of infectious bites per emerging mosquito (β) was multiplied by the emergence rate of mosquito vectors (E). If this product (βE) is divided by the human population size (N_h), we obtain the mean number of infectious bites that an average individual human receives, also referred to as the mean entomological inoculation rate (EIR) experienced by individuals in the community [73], [74]:(18)

In a human population composed of two distinct subgroups (ITN users and non-users), it is important to calculate separately the EIR experienced by each subgroup so that we can compare them. For either subgroup, this is a product of the total number of infectious bites upon humans that occur in the population as a whole (βE) and the fraction of biting exposure experienced by that particular subgroup of the population. Here also, the original forms of these equations [43] are replaced with explicit forms to express the availability of blood rather than the availability of attackable hosts, and consequently capture exposure to bites rather than exposure to attacks:(19)(20)

For purposes of estimating the likely impacts of interventions, it is imperative to know how much the exposure to bites from malaria-infected mosquitoes can change when an individual becomes protected by a preventative measure such as an ITN. Dividing equation 20 by equation 19 and substituting with equation 12 provides a solution which is consistent with the commonly accepted definition of personal protection against exposure to infectious bites [68], [75]:(21)

For integrated programs, involving the use of ITNs and odor-baited traps, there are several possible intervention package scenarios (Ω). Each package is explicitly defined by the ITN coverage (C_h), ITN properties (θ_Δ and θ_μ), number of odor-baited traps (N_t) and the mean availability (a_t) of those traps. For ease of comparison and interpretation, the impact of any intervention package, Ω, is expressed in terms of relative exposure to transmission intensity (ψ_Ω = EIR_Ω/EIR₀), where EIR_Ω is the mean exposure of humans in the presence of the intervention package and EIR₀ is the mean exposure of members of the same community when no intervention is present. We use the notation EIR₀ = EIR_h,u,0 to denote the EIR of all humans when no intervention is present, EIR_h,u,Ω to denote the EIR of humans without ITNs in a population with the intervention Ω and EIR_h,p,Ω to denote the EIR of humans with ITNs in a population with the intervention Ω. The mean EIR in the presence of the intervention package is therefore:(22)where C_h is the proportional coverage of the human population with ITNs.

The total benefits of any intervention package, Ω can then be apportioned to personal or communal protection benefits and expressed in terms of EIR relative to the baseline scenario with no interventions as follows:(23)for communal protection provided by the integrated intervention package to people who do not use ITNs, and(24)for combined personal and communal protection provided by the integrated intervention package to people who use ITNs.

Whereas people who do not use ITNs will benefit from only the communal protection provided by the integrated intervention package, those who use ITNs will benefit from both the personal protection provided by their own ITNs and the communal protection provided by the integrated intervention package. The contributions of personal and community-level protection to the benefits of ITNs have been discussed in detail elsewhere [43] and are therefore not the focus of this paper. Here, we express the influence of ITNs simply as the mean relative exposure of an average member of the community. This is calculated as the mean of the relative EIR of protected and unprotect hosts, weighted according to the proportions of the human population that they represent:(25)

When odor-baited traps are added to the intervention package alongside ITNs, we expect that the exposure of both net users and non-users to infectious mosquitoes is correspondingly reduced. Because ITNs are already widely used in Africa [29], the traps should be considered only as complementary interventions rather than as replacement for the ITNs. Their effects on transmission should therefore be evaluated in terms of the further transmission reductions they offer, relative to that which is provided by ITNs alone. To determine how much benefit the odor-baited traps would actually contribute towards the overall reductions generated by the combined intervention, the residual exposure experienced when the combined package is implemented is expressed relative to the residual exposure experienced when only nets at any given coverage (C_h) are used:(26)reflecting additional protection offered by odor-baited traps to communities using ITNs.

Because odor-baited traps are considered as a distinct host type (more specifically pseudo-hosts), we used this model to explore the hypothesis that their effects on malaria transmission will depend on how much they contribute to the total availability of all hosts for attack by malaria mosquitoes, which is equivalent to the proportion of the total available host resources covered or accounted for by the odor-baited traps (C_A):(27)

It is expected that as C_A increases, so will the impact of the traps on malaria transmission. With reference to these reformulated equations there are two possible ways to increase total trap availability (A_t) and therefore increase C_A. These include increasing the relative availability of individual traps (λ_t) or increasing the number of traps deployed (N_t). Similarly, with reference to the current definition of mosquito host-seeking processes, the relative availability of individual traps (λ_t) can be increased by ensuring high encounter rates and high attack probabilities relative to that of the preferred vertebrate hosts such as cattle and humans. Practical ways to effect such enhancements are outlined explicitly in the section entitled parameters describing odor-baited traps.

Baseline ecological parameterization of the model

In table 3, the ecological parameters and associated values used as well as the source references are outlined. As in the original model [43], a village with 1000 persons and 1000 head of cattle is considered. Parameter value for infectiousness of humans to mosquitoes (κ) was also set the same as in the original model (0.030). It was assumed that infectiousness of humans to mosquitoes is constant across the population, regardless of the impacts of vector control measures. Therefore any additional benefit that may be accrued by reducing this parameter once EIR drops below the threshold of 10 infectious bites per person per year [76] is ignored. To achieve baseline transmission intensities representative of places in Africa where malaria transmission is constantly intense [77], [78], we increased the mosquito emergence rate from the original value of 9 million [43] to 20 million, which resulted in baseline EIR values greater than 200 in the test scenarios, thus a typically challenging holoendemic scenario was represented.

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Table 3. Values and references for ecological parameters in the simulations.^a

https://doi.org/10.1371/journal.pone.0011573.t003

The daily survival probability of a resting mosquito was set to 0.9 while the daily survival probability of mosquitoes while foraging for blood or oviposition sites (P_ov) was set to 0.80, also consistent with published applications of the original model formulations [43], [44]. The baseline host defences of people who do not use ITNs, and of cattle, were assumed to be the same. Therefore, the probabilities for An. arabiensis and An. gambiae s.s. being diverted (Δ) or killed (μ) during attack on either non-ITN users or cattle was set as 0.1. This means 90% of all mosquitoes of these species would attack the hosts upon encountering them and thereafter 90% of those that attack the hosts will successfully take blood meals from them.

The mean availability of non ITN-users had been estimated for An. arabiensis on the basis of field estimates in a southern Tanzanian village at a time when less than 1% of the population used nets [79]. The study considered dissection based observations of the dilation status of ovariolar stalks in host-seeking female mosquitoes caught with human-baited light traps [79]. The number of successful feeds per day per host-seeking vector per human was therefore originally calculated as the inverse of the inferred host-seeking interval of 0.7 days divided by the human population size in the study area, which was 1212 at that time [80].

Reconsidering this estimate in the light of this revised definition of host availability for attack, this approach to parameterization now seems even more appropriate as the dissected unfed mosquitoes were sampled during the attack phase, before feeding and obviously before death. In fact, the availability value used in the original model should actually have been defined as successful attacks (rather than successful feeds) per day per host-seeking vector. For the purposes of this new model formulation, the parameter value therefore remains unchanged and was applied also to An. gambiae. The mean availabilities of humans to An. arabiensis and An. gambiae were then used to calculate the mean availability of cattle to attack by the same vector species. Based on equation 9, this was accomplished by calculating the product of these mean availabilities (a_h) and estimates of the relative availability of cattle (λ_c), which had earlier been derived from field studies of mosquito host preferences [46], [54]. Finally, the total availability of aquatic habitats (A_a) was set to 3, also unchanged from the previous application [43].

Parameters describing Insecticide Treated Nets

The intervention parameters and associated values used, as well as the source references, are outlined in table 4. We considered baseline scenarios to be communities lacking traps but where ITNs were either completely absent or being used by half of all age groups within the community. As in the original model, the effects of ITNs were quantified in terms of their ability to repel malaria vectors from humans and/or to kill the vectors whenever they attacked the net users. Though the World Health Organization, has to date approved seven different Long Lasting Insecticide Nets (LLINs), including interim approvals [81], we simulated scenarios with one long-lasting insecticidal net type, namely Olyset ® nets, whose properties are representative of the most commonly used LLINs in Africa. These LLINs are knitted from polyethylene fibres that have been impregnated with a first-generation synthetic pyrethroid, namely permethrin [82]–[84]. Apart from being toxic to mosquitoes, permethrin is also an excito-repellent, meaning that the nets also divert considerable proportions of these mosquitoes even before they can attack net users [82]–[87]. The parameter values used in the simulation were chosen such that they approximate the properties of Olyset ® nets under normal conditions of community use.

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Table 4. Values and references for intervention parameters in the simulations.^a

https://doi.org/10.1371/journal.pone.0011573.t004

Repellency of nets, which is measured as a reduction in the number of mosquitoes that enter human-occupied huts [88] when the nets are used by the occupants, is reflected in the excess diversion of mosquitoes from an ITN user (θ_Δ). Correspondingly, the excess mortality upon attacking the ITN user (θ_μ) is estimated as the excess proportion of mosquitoes entering those experimental huts that die attempting to feed on the hut occupants, relative to control huts. The parameter values of the selected representative net type were set to reflect the following: 1) diversion of 50% of all mosquitoes that encounter the net users (θ_Δ = 0.5), and 2) excess mortality of 70% of those mosquitoes attacking the net users (θ_μ = 0.7). These estimates were computed from reports of experimental hut studies previously conducted in the field [83]–[85], [89], [90]. As per equation 8, these diversion and mortality values mean that the nets would protect against 85% of all indoor malaria exposure (protection against bites = 100×(1−((1−0.5)×(1−0.7)) %).

ITN coverage in Africa is gradually improving and an increasing number of countries are achieving net coverage of 50% or more, especially for children under fives [29], [37], [91]. To achieve the full potential of nets, including valuable community-wide benefits, it is broadly agreed that reasonably high coverage of entire communities rather than just vulnerable groups is required [36], [43], [92], [93]. Therefore, consistent with the best estimates of the minimum level community-wide coverage required [43], [94], we simulated situations with 50% ITN use across all age groups to represent what is likely attainable in most African countries. In addition, we simulated situations with 80% ITN coverage to represent areas where ITN distribution and coverage in Africa have been highly successful and where existing net distribution and promotion mechanisms may guarantee such coverage levels [90].

Finally, the proportion of normal biting exposure of non-users that occurs indoors when nets would usually be in use (π_i) was set at 0.9 based on recent estimates for An. gambiae sensu lato from a malaria-endemic village in south eastern Tanzania [45], [68].

Parameters describing odor-baited trap technologies

A minimal diversion probability of 0.1 was assumed for mosquitoes encountering odor-baited traps, identical to baseline diversion probabilities from persons not using ITNs and also from cattle. Since there is no possibility of mosquitoes getting blood meals from the odor-baited traps, the probability of successful feeding upon the traps was set to be zero (φ_t = 0). Correspondingly, because traps retain and kill the captured mosquitoes, we set the probability of attack-related mortality upon them to be one (μ_t = 1). Considering the successive stages of host-seeking by a mosquito (Fig. 1), the relative availability of the traps (λ_t) could therefore be varied in different ways.

First, the encounter rate (ε_t) can be increased by making the traps easier for mosquitoes to find, either by placing them in locations close to breeding sites or by improving the attractants (baits) so that the range from which the traps are detected by host-seeking mosquitoes is extended. Moreover, changing the relative attractiveness of the traps to mosquitoes when compared to the attractiveness of actual human hosts, which is equivalent to changing attack probability (γ_t) could also lead to increased or reduced trap catches. However, given the very high attack probabilities assumed in this model, there is little scope for meaningfully increasing this parameter value. It is therefore likely that increasing encounter rates (ε_t) or the number of traps (N_t) are the primary means available to maximize total trap availability (A_t). We therefore hypothesize that these factors represent the key parameters that should be considered when outlining target product profiles for developers of odor-baited traps.

Few studies exist in which odor baits have been compared with humans under realistic field conditions. However in recent field evaluations in rural Tanzania, a mixture of synthetic attractants that mimic human odors, proved to be more attractive than humans to several genera of mosquitoes including malaria vectors [41]. These experimental prototypes attracted approximately four times as many Anopheles gambiae as an average human whenever the traps and the human were in separate huts 15 to 100 meters apart, but the humans remained more attractive whenever the two were side by side inside the same hut, resulting in increased exposure of the humans to mosquito bites [41]. This indicates that the synthetic odor blend most probably acts as a long-range cue, attracting more mosquitoes to the point source, at which the mosquitoes then choose the co-located human host based on stronger short-range, non-host-specific stimuli such as heat and water vapor.

These field estimates were therefore used to compute the mean availability of individual traps (a_t) using equation 10 by simply multiplying mean availability of individual humans (a_h) by a factor of four (λ_t = 4). All the relevant intervention parameters and associated values are also outlined in table 4.

Targeted positioning and delivery systems for odor-baited traps

By comparing the numbers of mosquitoes caught in huts where traps had been placed versus catches in huts where human volunteers slept [41], we estimated the relative availability of the odor-baited traps if such traps are evenly or randomly placed in a set of locations that are geographically distributed in the same way as the human population (λ_t = 4). In such a case of unbiased trap placement among human residences, encounter rates of the traps (ε_t) is simply a function of mean human availability (a_h) and the experimentally measured relative availability of traps (λ_t), which is primarily influenced only by the attractive range of those devices.

For ethical and safety reasons, however, odor-baited traps similar to the ones we have field-tested [40], [41], should never be deployed in such a manner that they are evenly distributed among humans because they emit long-range attractants which can increase exposure of nearby residents for the reasons described above (Sumaye et al., Unpublished). In practice it is impossible to guarantee the minimum distances required to exclude this possibility in even the most modestly clustered human settlements. It is therefore essential that the odor-baited traps are placed far from human residences and aggregations thereof. Fortunately this also offers an excellent means to enhance intervention efficacy and minimize costs.

The targeted placement away from houses is desirable not only to maximize safety but also to take full advantage of mosquito distribution patterns, which naturally present significant opportunities to dramatically enhance effectiveness of mosquito trapping programs. Heterogeneities in the transmission of vector borne infectious diseases including malaria are known to consistently follow the “80/20 statistical distribution” [63] meaning that at least 80% of transmission occurs in 20% or less of all locations. This well established feature clearly implies that deliberately biasing the spatial distribution of any intervention to the most intense foci of vector density, which correspond to locations with higher than average encounter rates and therefore increased availability of the traps, will have correspondingly enhanced impacts upon malaria transmission.

In this model, spatially biasing the location of the traps based on this well-established phenomenon would effectively result in a four-fold enhancement of relative trap availability because with such deliberately biased trap placement, the rates of trap encounter are enhanced four times. Unlike in the case of unbiased placement, the relative trap availabilities (λ_t) are therefore enhanced not only by their longer attractive range, but also by the increased probability that the mosquitoes will encounter those extended odor plumes. It therefore follows that in a situation where these particular traps are biased to locations with 80% of all mosquitoes, their relative availability increased a further four fold, which combined with the field estimates of the enhanced attractiveness yields relative availability of λ_t = 4×4 = 16.

While targeted placement of traps to enhance availability might be achieved by mapping the relevant area and conducting geographic rather than household-based entomological surveys, sufficient resources and institutional capacity to accomplish this are not available in the vast majority of African communities. Nevertheless, we suggest that enough is known about mosquito distribution to enable informal selection of appropriate sites with a reasonable degree of accuracy in most settings that we are familiar with. The kinetic definition of availability, which we have formulated here implies that the availability of the traps for host-seeking mosquitoes will always be higher in areas close to aquatic habitats as this is where the mosquitoes emerge from and also where they return to lay eggs and restart their next host-seeking phase in the beginning of each feeding cycle [61], [65], [95], [96]. Also, houses on the outskirts of aggregated human population such as towns and villages, or around breeding habitats within them [60]–[62], [97], [98] are always exposed to more mosquitoes than those in the centre because mosquitoes dispersing into such settlements inevitably feed predominantly on the hosts they encounter first which are, by definition, more available to them [96].

This quantitative and qualitative knowledge of mosquito dispersal processes suggests three alternative positioning strategies, which can be implemented even in the absence of fine-scale maps showing mosquito densities, and which can therefore also be used to achieve optimal targeting of the odor-baited traps (Figs. 2A–C). Firstly, where the community is small, tightly aggregated and surrounded by numerous and dispersed aquatic habitats (particularly where these are cryptic or unpredictably distributed) the best solution is probably to surround the perimeter of the settlement with traps (Fig. 2A).

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Figure 2. Alternative positional strategies for achieving optimal targeting of odor-baited mosquito traps.

The figure shows places where the odor baited mosquito traps should be located in different scenarios namely: A; where the communities are small, tightly aggregated and surrounded by large or numerous aquatic habitats, B; where habitats are relatively few and easily identifiable such as in arid-rural areas and C; in urban settings where the main aquatic habitats are surrounded by human settlements. This diagram is not drawn to scale and is limited to basic structural representations of spatial relationships between human settlements and mosquito larval breeding sites.

https://doi.org/10.1371/journal.pone.0011573.g002

Secondly, where habitats are relatively few in number and easily identifiable, as may be the case in arid rural areas [99], surrounding the breeding sites may offer an even more effective strategy (Fig. 2B). Urban areas where major areas of mosquito proliferation are usually surrounded by human settlement, rather than vice versa [97], [98], represent a situation where these two strategies coalesce and are essentially equivalent (Fig. 2C). It should therefore be possible, even without detailed maps of mosquito densities, to selectively position traps in ways that enhance their relative availabilities at least as well as the four-fold increase modeled here.

Conclusions

Odor-baited mosquito traps could provide substantial protection against malaria in their own right and could augment benefits already achieved with ITNs if deployed as a complementary intervention. For this strategy to succeed, we propose that the following three key criteria should be met: 1) that the odor-baits should be considerably more attractive to malaria vectors than humans, 2) that the traps should be located in areas where host-seeking mosquitoes are concentrated and 3) that they need to be cheap and easy to deploy at a rate of 20–130 traps per 1000 people. Finally, if efficacious interventions matching this target product profile were developed, we recommend that the most appropriate way to deploy them effectively and sustainably would be through vertical rather than horizontal delivery mechanisms, which will require strong technical support from central authorities such as National Malaria Control Programmes, as well as broad progress towards improved governance and capacity of local authorities to implement such programmes on the ground.