Combining indoor and outdoor methods for controlling malaria vectors: an ecological model of endectocide-treated livestock and insecticidal bed nets
© The Author(s) 2017
Received: 23 November 2016
Accepted: 24 February 2017
Published: 13 March 2017
Malaria is spread by mosquitoes that are increasingly recognised to have diverse biting behaviours. How a mosquito in a specific environment responds to differing availability of blood-host species is largely unknown and yet critical to vector control efficacy. A parsimonious mathematical model is proposed that accounts for a diverse range of host-biting behaviours and assesses their impact on combining long-lasting insecticidal nets (LLINs) with a novel approach to malaria control: livestock treated with insecticidal compounds (‘endectocides’) that kill biting mosquitoes.
Simulations of a malaria control programme showed marked differences across biting ecologies in the efficacy of both LLINs as a stand-alone tool and the combination of LLINs with endectocide-treated cattle. During the intervals between LLIN mass campaigns, concordant use of endectocides is projected to reduce the bounce-back in malaria prevalence that can occur as LLIN efficacy decays over time, especially if replacement campaigns are delayed. Integrating these approaches can also dramatically improve the attainability of local elimination; endectocidal treatment schedules required to achieve this aim are provided for malaria vectors with different biting ecologies.
Targeting blood-feeding mosquitoes by treating livestock with endectocides offers a potentially useful complement to existing malaria control programmes centred on LLIN distribution. This approach is likely to be effective against vectors with a wide range of host-preferences and biting behaviours, with the exception of species that are so strictly anthropophilic that most blood meals are taken on humans even when humans are much less available than non-human hosts. Identifying this functional relationship in wild mosquito populations and ascertaining the extent to which it differs, within as well as between species, is a critical next step before targets can be set for employing this novel approach and combination.
The burden of malaria has been reduced considerably in the last 15 years following sustained, large-scale mosquito control efforts . However, the continued success of vector control programmes is threatened by several concomitant factors. The biggest threat has been the emergence and rapid spread of insecticide resistance among the principal vector species. Resistance exists to all classes of chemical insecticide currently endorsed by the World Health Organization (WHO) for mosquito control, with numerous mosquito populations across sub-Saharan African and Asia demonstrating resistance to multiple chemical classes at once [2, 3]. Behavioural changes have also been observed among malaria vectors whereby species (or sibling species) that were previously inclined to bite people indoors during sleeping hours now bite at different times of the day and/or bite outdoors [4–6]. Despite being a long-recognized threat to malaria vector control [7, 8], it remains unclear whether this change is phenotypic or genetic. Additionally, the proportional composition of overlapping mosquito species (or sibling species) has drastically shifted in recent years to favour mosquitoes that have always been more inclined to bite outdoors and that are less discerningly anthropophagic . An accelerated research effort to develop alternative control methods that are not attenuated in their effect by extant resistance or behavioural resilience is strongly advocated.
One such development is the treatment of livestock with insecticides. Although harmless to the animals themselves, these ‘endectocides’ kill mosquitoes following the blood meal. The treatment of livestock with pour-on insecticides was first widely used for the control of ticks  and then tsetse flies . Recently, there has been increased interest in the use of ivermectin: this is an anthelminthic used at large scale for the control of river blindness in humans and veterinary diseases in livestock. Its function of killing mosquitoes on ingestion is coincidental and was first observed only recently . A shortcoming of ivermectin for mosquito control is the rapidity with which it is metabolized, which means frequent application would be needed . However, a study by Poche et al.  recently demonstrated highly effective mosquitocidal properties of diflubenzeron, eprinomectin and fipronil when topically or orally administered to cattle. They demonstrated significant mortality (50%) among mosquitoes within 2 days of feeding on cows after up to 1 month of being orally treated with 1 mg/kg fipronil.
The next stage for assessing the suitability of this approach for controlling malaria vectors is to identify when and where its implementation would have maximal benefit as part of an integrated vector management strategy together with the current malaria control mainstay of long-lasting insecticidal nets (LLINs). Increasingly, mathematical models have become integral components of formulating infectious disease control strategy , especially so in the context of malaria because of the long history this analytic method has had in describing Plasmodium falciparum transmission . Here, a mathematical model adapted from  is described and used to project the anticipated malaria control efficacy of complementing LLINs with endectocides. Simulations are designed to account for a diverse range of mosquito-biting behaviours.
The qualitatively different behavioural responses (parameterization and associated vector behaviours) described by the new formula
(adapted from )
Holling’s Type I
α = 1
β = 1
Indiscriminate, or vector biting that is consistent (proportionate) across relative availabilities of alternative hosts
Holling’s Type II
α < 1
β ≥ 1
An anthropophilic vector which takes most of its blood meals on humans even when humans are less available than other hosts, and when humans and non-humans are equally available, almost all blood meals are taken from humans
Holling’s Type III
α ≥ 1
β > 1
This is the pattern expected with a learned behaviour, such that female mosquitoes learn to prefer the more common Type of host
Inversion of Holling’s Type II
α > 1
β ≤ 1
A zoophilic vector is disinclined to bite humans until they constitute all but the only available blood source
Inversion of Holling’s Type III
α ≤ 1
β < 1
HBI saturates and becomes relatively invariant when humans and non-humans are at similar availability. This is analogous to ‘negative prey switching’ whereby the ‘predator’ consumes disproportionately less of the more available ‘prey’ . Eventually, when non-humans become vanishingly rare, the HBI is forced to increase sharply to unity
Model parameter definitions, values and sources
Value [cited literature]
Transmission coefficient (vectors → hosts) = bite rate (day−1) × transmission probability
0.1 = 1/3 × 0.3 
Transmission coefficient (hosts → vectors) = bite rate (day−1) × transmission probability
0.007 = 1/3 × 0.02 
Ratio of vectors to humans
Varied in simulations; values in figure legends
Clearance rate of symptomatic infection (day−1)
Clearance rate of asymptomatic infection (day−1)
Level of reduced susceptibility to secondary infection
Full susceptibility reversion rate (day−1)
Birth and death rate of humans (day−1) (i.e., stable population)
Birth (or maturation) and death rate of vectors (day−1) (i.e., stable population)
Adjustment factor for asymptomatic transmissibility to vector
Rate of parasite development within vector (day−1)
Long-lasting insecticidal nets have the dual function of reducing the bite rate on humans and killing mosquitoes that come into contact with the insecticide with which they are treated. Both of these effects wane over time as the net accumulates holes and the insecticide loses potency. Recent studies with modern LLINs suggest a range of efficacy half-lives with a median value of approximately 2 years (i.e., after this period, the efficacy of protecting humans and in killing mosquitoes is 50% the original rate of a brand new net) [34, 35]. Similarly, estimates of initial efficacy of LLINs, in terms of mosquito mortality and personal protection, differ between studies. Universal (100%) coverage of a net that is (initially) 75% effective in personal protection and that results in 50% mosquito mortality within one day of contact fall within the reported range and are assumed here [36, 37]. To ensure sustained protection, current WHO guidelines recommend replacement of LLINs every three years. In practice, however, an interval of four years is probably more common, and so this is the frequency assumed in simulations.
Studies describing longitudinal endectocidal activity are scant; however, the study of Poche et al.  describe a maximum of 100% mosquito mortality following ingestion of blood from newly treated cattle and a half-life of between 21 and 28 days for 1.5 mg/kg oral fipronil. Here, a conservative estimate of 21 days is simulated. A wide range of different frequencies and coverage levels of endectocide are simulated in order to provide the first estimates of target levels with which to complement current policy goals for LLIN coverage.
Both the reduced rate in human-biting and the increased rate of mosquito mortality that results from simulated use of LLINs are assumed to exponentially decay in efficacy over time. Similarly, the increased mosquito mortality resulting from bites on livestock that are treated with endectocides is assumed to exponentially decay over time. Hence, b H * = b H × [1 − C 1 × (1 − ln(2)/730) t ] denotes the diminished transmission potential from vector to human resulting from a reduced bite rate through LLINs (with an equivalent expression for b V ); and µ V * = µ V + 1/3 × [p H × C 1 × (1 − (ln(2)/730)) t + (1 − p H ) × C 2 × (1 − (ln(2)/21)) t ]. Control efficacy on mosquito mortality is a product of 1/3 because it is assumed that these vectors bite at a maximum of every three days on average. The square bracket in the equation describing mosquito mortality contains the increased mortality that comes about through contact with LLINs (the first half of the expression that is a product of C 1 : coverage—here ‘1’—multiplied by maximum efficacy of a new LLIN—here ‘0.75’) as well as through biting an endectocide-treated animal (the bold-font second half of the expression that is a product of C 2 : coverage—a full range from ‘0’ to ‘1’ is explored—multiplied by maximum efficacy of newly applied endectocide—here ‘1’). ‘t’ denotes the time-point (in days) after control distribution, i.e. allows for a decay in efficacy of the controls over time. With each round of newly distributed LLINs, any remaining control impact from prior rounds of LLINs are zeroed. Similarly for endectocidal applications. This simplification will only act to produce more conservative estimates in efficacy (for example, because some livestock that are not treated in the current round may have remaining endectocide).
For direct comparison of control efficacy across the different mosquito biting Types, baseline (pre-control) infection level was standardized at 50% malaria prevalence. This was achieved through adjustment of the vector-to-human ratio, m, until each control scenario was initiated under the same prevalence level. The alternative was to maintain a constant m but allow for different initial infection prevalence between the different scenarios of vector-biting behaviour; but it was deemed preferable to standardize models according to the more epidemiologically relevant metric. Details of precise m values needed to generate 50% prevalence are provided in the legends of the associated results plots. The model was implemented in Berkeley Madonna software using the Runge–Kutta 4 method of numerical analysis.
When specifically considering LLIN control of symptomatic infections (right-hand column of Fig. 2), rebounding prevalence exceeded pre-control levels after bed net efficacy was diminished. For some mosquito-biting ecologies, this rebound was substantial (up to a 2.5-fold increase relative to pre-control for a Type IV) as was the time period over which symptomatic prevalence exceeded pre-control levels (constituting 33% of a 4-year LLIN cycle for a Type IV mosquito).
For most mosquito-biting ecologies, even modest coverage levels of endectocide-treated cattle provided considerably improved malaria control efficacy. For an indiscriminate mosquito (with Type I response, i.e. the standard assumption of other malaria models that cater for non-human biting), the control combination including 80% coverage of endectocides maintained total malaria prevalence at below 0.2% during the 4-year cycle. Comparable gains in combined control were obtained for mosquitoes that displayed switched host preference as a function of relative host availability levels (prevalence was maintained below 1.7 and 0.2% for Type III and Type V, respectively). Intuitively, malaria transmitted by zoophilic mosquitoes (Type IV) experienced the greatest decline with endectocidal applications (maintained below 0.001%) whereas the least benefit to malaria control (almost negligible) was provided when mosquitoes were more anthropophilic (Type II). The qualitative nature of these results was not found to be sensitive to the parameters governing biting behaviour within the respective bounds of the biting Types (Additional file 1).
In recent years, malaria control successes have brought to the fore plans for elimination, and rekindled hopes of eradication. Malaria control is largely dependent on mosquito management with LLINs or indoor residual spray (IRS). However, the spread of pyrethroid resistance challenges the sustainability of these current control mainstays. As well as new insecticides for IRS and LLINs, there is the need to reduce dependence on these two technologies and to find new ways to attack adult Anopheles malaria vectors. The current study constitutes the first theoretical examination of the combined use of endectocide-treated livestock with LLINs in order to assess the projected level of improvement in malaria control.
Targeting livestock-biting behaviour for controlling malaria mosquitoes is shown through simulation to have a potentially excellent synergy with LLINs for reducing malaria prevalence. Although it seems intuitive that adding more vector control tools should have the inevitable effect of improving upon efficacy, this is by no means a foregone conclusion. For example, previous theoretical studies have demonstrated that incorporating mosquito larvae breeding site management does not necessarily improve control projections when used as a complement to insecticidal nets unless breeding sites are already vanishingly rare and/or when nets have drastically compromised efficacy . In terms of the most popular integrated vector management strategy in the world, LLINs and IRS, models have given conflicting results with some projections highlighting potential for interference between insecticidal modes of action actually reducing the benefit achieved with LLINs alone . There is mounting evidence from the field to challenge the usefulness of this combination in some epidemiological/entomological settings [40–42], particularly when the additional control methods imply substantial additional costs.
In the current analysis, it was demonstrated that the epidemiological benefit of endectocide-treated cattle as an addition to LLINs is contingent on both the mosquito-biting ecology of local vectors and the intended purpose of the programme (being either morbidity reduction or elimination). Intuitively, endectocidal applications improve upon LLINs to the greatest degree when local vectors are more zoophilic (Type IV). Relatively modest frequencies of endectocidal application (in the order of three times per year) can substantially improve control efficacy when local vectors exhibit this behaviour. However, mosquitoes do not need to be particularly zoophagic for this control strategy to drastically improve projected control efforts—malaria spread by vectors that are indiscriminate in their host choice (Type I) is also controlled effectively with the integrated strategy. It should be emphasized that the current study is the first to explore the effects of combining these vector control methods, and as such, quite a simplistic model was used to present the results as transparently as possible. In order for the results described here to inform operational strategy, a more biologically detailed epidemiological model would be warranted, and this constitutes important future work. Further work could include adaptations of the mosquitoes to the reduced host availability resulting from LLINs. By reducing the proportional composition of humans, it may be posited that bed nets act to divert bites onto other host species—although, see Hii et al.  who do not show this effect. Importantly, however, this potential addition to future models would only have the effect of potentiating the control combination explored in the current analysis; it should be reiterated that the substantial benefits of this integrated strategy are likely only downplayed by the conservative estimates produced in this analysis.
To explore temporal dynamics of infection control, simple, exponential decay functions to describe the reduced efficacy of controls over time were included. Although more complicated functions have been discussed previously in the context of waning bed nets and IRS , exponential decay is the more popular method of incorporating this effect. Future work may be warranted to explore the impact of different decay functions for operational strategy, as more longitudinal efficacy data become available.
Waning malaria control inadvertently exacerbating symptomatic disease is the subject of discussion of several mathematical models. However, there is surprisingly little evidence of this phenomenon in practical reports from the field. In Africa, withdrawal of vector control has tended to lead to an eventual return to pre-control levels of infection prevalence , but changes in symptomatic cases are not reported. It is possible that this bounce-back is an artefact of models (including the one presented here). It is also possible that whatever causes the withdrawal or suspension of vector control may also weaken the surveillance needed to detect such a rebound, at least during the period immediately after withdrawal.
Regardless, if the objective of the programme is morbidity reduction, endectocide-treated cattle may additionally benefit a programme by reducing any temporary undesirable consequences of fluctuating levels of control on projected symptomatic infection rates. It can ameliorate disease when a control campaign is underway while also improving chances of achieving the goal of elimination. In other words, if one desired outcome of a given programme is morbidity reduction in the shorter term prior to elimination, there may be even greater justification for complementing LLINs with endectocide-treated livestock. With the current analysis, the first estimates of integrated vector management efficacy are provided for this novel pairing of interventions. Additionally, a framework is described for assessing the anticipated impact of these approaches on the control of a disease that is spread by vectors with increasingly recognized diverse feeding behaviours. Given the level of impact that this neglected behaviour is projected to have on disease intervention efficacy, generating empirical data to determine mosquito-biting behavioural Types constitutes an important future research goal.
LY conceived of the study, constructed and analysed the model and wrote the manuscript. MC and JL contributed to interpreting model findings and writing the study. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
The Medical Research Council, The Newton Fund and The Wellcome Trust provided funding through a joint Grant (MC_PC_15097) to LY.
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