Controlling Malaria Using Livestock-Based Interventions: A One Health Approach

Where malaria is transmitted by zoophilic vectors, two types of malaria control strategies have been proposed based on animals: using livestock to divert vector biting from people (zooprophylaxis) or as baits to attract vectors to insecticide sources (insecticide-treated livestock). Opposing findings have been obtained on malaria zooprophylaxis, and despite the success of an insecticide-treated livestock trial in Pakistan, where malaria vectors are highly zoophilic, its effectiveness is yet to be formally tested in Africa where vectors are more anthropophilic. This study aims to clarify the different effects of livestock on malaria and to understand under what circumstances livestock-based interventions could play a role in malaria control programmes. This was explored by developing a mathematical model and combining it with data from Pakistan and Ethiopia. Consistent with previous work, a zooprophylactic effect of untreated livestock is predicted in two situations: if vector population density does not increase with livestock introduction, or if livestock numbers and availability to vectors are sufficiently high such that the increase in vector density is counteracted by the diversion of bites from humans to animals. Although, as expected, insecticide-treatment of livestock is predicted to be more beneficial in settings with highly zoophilic vectors, like South Asia, we find that the intervention could also considerably decrease malaria transmission in regions with more anthropophilic vectors, like Anopheles arabiensis in Africa, under specific circumstances: high treatment coverage of the livestock population, using a product with stronger or longer lasting insecticidal effect than in the Pakistan trial, and with small (ideally null) repellency effect, or if increasing the attractiveness of treated livestock to malaria vectors. The results suggest these are the most appropriate conditions for field testing insecticide-treated livestock in an Africa region with moderately zoophilic vectors, where this intervention could contribute to the integrated control of malaria and livestock diseases.

The model for untreated livestock used the latter expression to derive j, where x is the proportion of the vector mortality in the absence of available livestock that is unrelated with searching for a bloodmeal host (and, conversely, 1-x, also designated by  , is the proportion of vector mortality in the absence of available livestock related with host search).
The values of j were chosen to obtain h  =0.1/day (which is illustrative and within the limits of recorded field valuesvector life expectancy of 10 days), in a village with 100 persons and where the vector feeds once every two days (j=0.1105, 0.2 and 1 for A h =0.9, 0.5 and 0.1, respectivelywhich corresponds to A l =0.1, 0.5 and 0.9, respectively, in the baseline scenario of x= =0.5).

S3.2. Insecticide-treated livestock model parameterization for Pakistan and Ethiopia
The parameter values used to explore the effects of insecticide-treated livestock are listed in Table 2. Most values were either extracted or derived from empirical data from the index studies in the NWFP of Pakistan (ITL trial by Rowland et al. [4]) and in the Konso district of South-west Ethiopia (field study by Franco [5]), or from previous studies within or near the area of the index studies. When data for a parameter were available from more than one published study, the simulations used the estimates from the studies that were most recent and/or conducted in areas within or closest to the areas of the index studies.

Rational for selection of Plasmodium falciparum
We model infection by Plasmodium falciparum because it is the most serious form of malaria infection and has no relapses, unless due to treatment failure, while with P. vivax the more frequent relapses may obscure the effects of the intervention, and other species are less prevalent. Additionally, in the Ethiopian setting most cases were due to P. falciparum [5]. Although in the Pakistan trial setting, P. vivax infections were more frequent [4], for comparison purposes, only the trial data for P. falciparum were used in the simulations.

Rational for selection of the species of malaria vectors
Pakistan: In the area of the Pakistan ITL trial the main malaria vectors were An. culicifacies and An. stephensi [6]. The simulations considered only An. culicifacies because this species is more anthropophilic, has a longer life expectancy, and has been implied as the most important vector species in studies done in Punjab Province, near the ITL trial study area [7]. We are therefore simulating a worse-case scenario regarding the vector species. Ethiopia: The model was fitted to An. arabiensis, as this is known to be the most important malaria vector in the study area, as well in the rest of the country [8,9,10].

Malaria prevalence in the study areas
Pakistan: The prevalence of P. falciparum infection in people in non-intervention villages during the ITL trial, ranged from 0.3% to 7.8% (M. Rowland, unpublished data). The simulations were conducted using baseline infection prevalence in people of 6%. This higher end range was chosen for three reasons: (1) it fell within the observed prevalence range; (2) however, as the villages chosen for the ITL trial had been subject to recurrent indoor spraying campaigns [4] 1 , the observed prevalence range was on average lower than expected in the majority of communities not experiencing regular vector control interventions and so, to understand the potential effects of the ITL intervention it is important to examine the higher prevalence settings as that enables quantifying the full potential public health benefits of targeting livestock; (3) from a theoretical perspective, the chosen starting condition allows examining a greater range of prevalence dynamics than starting at the lower end of the observed prevalence range.
Ethiopia: To the best of our knowledge at the date of this study, no data existed on the precise prevalence of Plasmodium spp. infection in the Ethiopian setting. However, since the figures were likely to be higher in Ethiopia than in Pakistan, simulations were done with a conservative baseline prevalence of infection in people of 10%. The corresponding predicted prevalence of sporozoite infection in mosquitoes was 0.38 %. This is consistent with field estimates in a village (Fuchucha) of the Ethiopian setting, where Tirados et al. [10] found that the P. falciparum sporozoite prevalence in samples of An. arabiensis was 0.38% and 0.18%, for mosquitoes attracted only to human or only to cattle baits, respectively (the overall P. falciparum sporozoite prevalence was 0.33%). 2

Human recovery rate from infection (r)
The human recovery rate from infection is given by 1/(average duration of infection in humans). The average duration of infection was based on the time elapsed since start of malaria symptoms until arriving at a health facility to receive treatment. During the Pakistan ITL trial this would take around two weeks (M. Rowland, unpublished data), and was inflated to 21 days to account for situations where it may have taken longer until receiving treatment. The same baseline value was assumed for Ethiopia, to facilitate the comparison of the predicted results with the Pakistan setting. This corresponds to a recovery rate of 0.05/day.

Rate at which infected mosquitoes become infectious (  )
The rate at which infected mosquitoes become infectious is given by 1/(average duration of latent period in vector), which was estimated using Moshkovsky's formula [11] for P. falciparum: latent period = 111/(T-16), 18<T<30, where T is the mean temperature in Celsius. The temperature data used were recorded near the Pakistan ITL trial setting at the Peshwara Meteorological Station, and in the center of the Ethiopian setting at the Karat Meteorological Station, and were obtained by personal communication with the National Meteorological Station in each country [5].
Pakistan: The average of the monthly mean temperatures recorded in Peshwara during the three years of the ITL was 22.3 ºC, which predicts a latency period of 17.5 days (range: 6.6 days in June to 18.9 days in April), giving  =0.057/day.

Ethiopia:
The average of the monthly mean temperatures recorded in Karat during the year of the index study was 23.1 ºC, corresponding to a latency period of 15.6 days (range: 11.9 days in March to 19.0 days in June), giving  =0.064/day.

Infection probability of humans (b)
The value of the infection probability of humans was based on findings from two separate studies where 5 out of 10 volunteers have developed parasitaemia after being bitten by one or two An. stephensi infected with P. falciparum [12,13]. No data were found for An. culicifacies, and therefore the An. stephensi data were assumed. Similar patterns of sporozoite transmission between An. stephensi and An. gambiae have been proposed [14]. Accordingly, b was set to 0.5 for both the Pakistan and Ethiopian simulations.

Infection probability of vectors (c) and relative density of vectors to humans (N v /N h )
As in previous vector-borne disease models [e.g. 15,16], the values for the infection probability of vectors (c), and the relative density of vectors to humans (N v /N h ) were chosen to produce malaria prevalence levels similar to the observed in the study areas, giving c=0.95, N v /N h =50 in Pakistan, and c=0.07 and N v /N h =15 for Ethiopia. Also, it was assumed that the density of vectors pre-intervention was at equilibrium.

Vector biting rate (a)
The vector biting rate on any host (a) was estimated assuming that the interval between bloodmeals on any host corresponds to the duration of the vector gonotrophic cycle (g).
Pakistan: The mean duration of the gonotrophic cycle for An. culicifacies was based on a study conducted in the Pakistan Punjab Province near the ITL area, that determined that after the first gonotrophic cycle which may take 4 days, the other cycles took 2 days in Summer (from Aug -Oct), and 3 days in Winter (Nov-Dec) [17].
Ethiopia: Findings from a study done in Gambella, an Administrative Region west bordering the Konso District, suggested a 2-days interval between feeding and oviposition for An. arabiensis [18]. Studies in North-Eastern Tanzania demonstrated a 3-days interval for the closely-related An. gambiae s.s. [19] and An. funestus [20]. In a later study, also in Gambella, hypothetical sporozoite prevalences have been estimated using a 2 to 3-days interval [21].
Accordingly, for both Pakistan and Ethiopia simulations, g was set to 2.5 days, giving a= 0.4/day.
The vector natural mortality rate ) ( 0  is given by 1/(average vector life expectancy), which was derived with the standard formula [22,23]: where p is the probability of daily survival, Pr is the proportion of parous female mosquitoes, and g is the mean duration of the gonotrophic cycle. It is valid to use the proportion parous to determine vector survival providing the following are observed: the population has reached a stationary age distribution; the survival rate is the same for all age groups; different age groups are sampled with similar efficiency; and the gonotrophic cycle duration is known and is constant [24]. Although in reality these conditions are rarely met, they are assumed to have been the case, as done in previous zooprophylaxis models. In both the Pakistan and Ethiopian settings the proportion parous was determined by the authors (Rowland et al. [4], and Taye et al. [25], respectively) using the ovarioles tracheolar method of Deltinova [26].

Density of livestock and human hosts (N l , N h )
Since for the purpose of the simulations it is sufficient to use relative density of hosts, a density of 100 persons/hectare was considered, for illustrative purposes. The relative density of livestock to humans was 0.14 in the Pakistan [4] and 1.13 in the Ethiopian [5] index study settings.
The present work accounts not only for cattle but also for other types of livestock, namely sheep and goats, as in the Pakistan and Ethiopian settings these were the alternative sources of bloodmeal for malaria vectors and were also treated with insecticide. For simplicity, it was assumed that one head of cattle was equivalent to one sheep or goat.
The relative availability of each of these animal types may however be different, not only because different animal types may be kept in different locations (at different distances from people's sleeping room and from vector breeding sites), but also because the vector's feeding preference and even feeding success may differ between animal types. For example, a study in Pakistan has found that, despite malaria vectors preferred to feed on goats than on cattle, feeding success was smaller on the former than on the latter hosts [27]. Such differences could be accounted by explicitly decomposing the availability term to equal the sum of the availabilities of each of these animal kinds, weighted averaged by their proportional abundance. The proportional availability of each animal type could be estimated if knowing the proportion of blood-meals taken upon each animal type. Alternatively, one could roughly assume that one head of cattle is equivalent to two sheep/goats, as done in experimental studies [28]. In the context of the present model, changing the assumptions about the relative contribution of each animal type to the overall abundance of livestock hosts would change: the relative density of animals per human, the estimated host availabilities, the HBI, and the availability scaling factor j, consequently affecting also the predicted vector mortality due to host search.
For the Pakistan simulations the implications would be minimal because most livestock were cattle. For Ethiopia, however, the impact would be greater, as the density of sheep/goats was more than twice than cattle. The implications of these different assumptions are described elsewhere [5], where comparisons were made of the above mentioned parameters when considering that (i) one head of cattle is equivalent to one sheep/goat, like done in the present manuscript, or (ii) one head of cattle is equivalent to two sheep/goats, or (iii) when considering only cattle. Basically, from i) to ii) and from ii) to iii), the values of the relative density of livestock/human would decrease, while the relative availability of livestock per humans, HBI, and j would increase.

Availability of livestock and human hosts (A l , A h )
i) The relative availability of livestock to humans ( h l A A / ) in a given setting can be estimated from the relative abundance of hosts and the HBI, using the formula based in Sota & Mogi [29]: Since there were no data on the HBI for the Pakistan ITL trial area, nor for the whole of the Ethiopian study area, the A l /A h was estimated using the relative abundance of hosts and HBI from previous studies conducted in the Pakistan Punjab Province near the ITL area (study in 1978 by Reisen and Boreham [6]), and in the Ethiopian Fuchucha village, within the index study area (study in 2003 by Tirados et al. [10] iii) To transform the proportional availabilities into the absolute availability values required for estimating s  , a scaling factor (j) was used, that was derived in a similar way to that for the untreated livestock model. Here, an analytical expression was derived for j that allows this parameter to be estimated for any setting with known abundance of hosts (N l and N h ), HBI (which enables estimating the proportional availability of hosts, A l and A h ), vector biting rate (a), and proportion parous (which enables estimating the natural vector mortality rate, 0  ), and a hypothetical or estimated m  .
Knowing that where the last term is the background vector search-related mortality (i.e. s  when no livestock are treated with insecticide), by solving for j it is possible to derive the following expression: the expression for j becomes equivalent to: The model used the latter expression for j, where ' x is the proportion of the vector natural mortality ( 0  ) that is unrelated with searching for a bloodmeal host (and, conversely, ' 1 x  , also designated by '  , is the proportion of the vector natural mortality related with host search).
Pakistan: The estimated A l /A h was 53.24 for An. culicifacies (Table S1).
Ethiopia: From the estimated A l /A h of 0.94 for An. arabiensis it is noticeable that, despite in Fuchucha livestock were ~50% more abundant than humans, the proportional availability of livestock (A l =0.48) was slightly lower than that of humans (A h =0.52) (Table  S2), which is consistent with the anthropophilic behaviour that has been demonstrated for An. arabiensis in the study area [10].

Vector minimum mortality rate ( m  ) and search-related mortality ( s  )
The vector minimum mortality rate ( m  , when there are no hazards due to searching for a bloodmeal host) was conservatively assumed to be half of the average vector natural mortality ( 0  ) observed in Pakistan and also in Ethiopia (i.e. ), which results in m  = s  pre-intervention=0.11/day for An. culicifacies and 0.06 for An. arabiensis (corresponding to a maximum longevity of 9.26 and 16.02 days, respectively).
A sensitivity analysis was done to access the impact that alternative relative magnitudes of m  and s  could have on the predicted outcomes, by exploring a conservative wider range than the one that is likely to occur in many natural settings. For that purpose, parameter ' x was varied from 0.10 to 1 (i.e. '  varied from 0.90 to 0), which corresponds to m  varying from 0.022 to 0.220 /day for An. culicifacies, and 0.012 to 0.120/day for An. arabiensis (background s  varying from 0.198 to 0, and 0.108 to 0, respectively), using the values for 0  , a, N h , N l , A h and A l in Table 2.

Vector human blood index (HBI)
The HBI for the vector in each setting was estimated using the A l /A h derived above from data on previous studies [6,10] and the N l /N h from the index studies [4,5], using the standard formula: Pakistan: The predicted HBI for An. culicifacies in the ITL trial setting (11.8%) was more than twice the HBI that had been estimated near the trial study area in the past (4.8% [6]) (Table S1). Such difference may be due to the higher relative density of humans:livestock during the ITL trial setting, which was also more than the double than during the previous study by Reisen and Boreham [6].
Ethiopia: The predicted overall HBI for An. arabiensis in the study area (49%; 95% CI= 39%-64%; Table S2) is concordant with previous estimates of HBI for Fuchucha (~49% by Habtewold [9]) and for other areas in Ethiopia (~40% by Hadis et al. [30]).   [5]. The remaining values were derived as illustrated with the slashed arrows and explained in the text, except '  which was hypothetically set to 0.5. The full arrows denote parameters values that were assumed to be the same in the index study area (Konso district) as in previous studies in within or nearby areas. N l /N h is the mean ratio of the number of animals per person calculated from the number of animals/person in each individual household. In the study by Tirados et al. [10] (a) all the households of the Fuchucha village were sampled, while in the index study (d), that includes Fuchucha plus 7 other villages (Dokatu, Duraite, Nalaya Segen, Sorobo, Gamole, Buso, Mechelo, and Baide), only some houses were sampled in each village, and therefore the sampling weighted mean N l /N h is presented. The weight of each village was calculated dividing the total number of households in a village by the number of households interviewed in that village. Inside brackets are 95% CI.

Insecticidal probability (k)
Our model assumes the insecticide effects (insecticidal and diversionary probabilities) are constant, therefore reflecting average values of what would be observed throughout the year. The insecticide direct lethal effect upon vectors exposed to treated livestock (denoted as insecticidal probability, parameter k) was estimated based on whole-animal bioassays of deltamethrin applied to cattle in Pakistan, where the proportion of female anopheline mosquitoes dead or unfed was ~85% on the day after treatment, decreasing to 50% after two weeks [31]. To account for the decay of insecticide residual activity, the k value was estimated as the weighted arithmetic average ( k ) of the insecticide lethal probability observed in the bioassay, calculated over the eight month period of active transmission of P. falciparum in the Pakistan trial villages (July to February, 245 days [5]). We considered three rounds of insecticide treatment of livestock during that period, with 6 weeks interval between rounds, like in the trial [4]. Namely, k was calculated as: is the frequency of each k value during the active transmission period (i.e. ) (k f = number of days when a given k value was observed divided by 245 days).
Unfortunately, the available bioassay data for the proportion of anopheline mosquitoes dead or unfed could not be dissociated, and therefore it is not possible to know the actual proportion dead/knockdown and the proportion unfed. Given this, the true observed insecticidal probability is likely to have been smaller than our estimated k of 0.12. Accordingly, throughout the manuscript we refer to a slightly smaller estimated k of 0.10.