Coverage and system efficiencies of insecticide-treated nets in Africa from 2000 to 2017

Abstract

Insecticide-treated nets (ITNs) for malaria control are widespread but coverage remains inadequate. We developed a Bayesian model using data from 102 national surveys, triangulated against delivery data and distribution reports, to generate year-by-year estimates of four ITN coverage indicators. We explored the impact of two potential 'inefficiencies': uneven net distribution among households and rapid rates of net loss from households. We estimated that, in 2013, 21% (17%–26%) of ITNs were over-allocated and this has worsened over time as overall net provision has increased. We estimated that rates of ITN loss from households are more rapid than previously thought, with 50% lost after 23 (20–28) months. We predict that the current estimate of 920 million additional ITNs required to achieve universal coverage would in reality yield a lower level of coverage (77% population access). By improving efficiency, however, the 920 million ITNs could yield population access as high as 95%.

DOI: http://dx.doi.org/10.7554/eLife.09672.001

Introduction

Insecticide-treated nets (ITNs), which comprise conventional (cITNs) and long-lasting insecticidal nets (LLINs), are the single most widely used intervention for malaria control in Africa, proven to significantly reduce morbidity and mortality via direct protection and community-wide reductions in transmission (Lim et al., 2011; Lengeler and Lengeler, 2004; Eisele et al., 2010; Killeen et al., 2007). The World Health Organization (WHO) promotes a target of universal coverage for all populations at risk with either ITNs or indoor residual spraying (IRS), with the former representing the primary vector control tool in nearly all endemic African countries (WHO, 2013a). The international community has invested billions of dollars in the provision of at least 700 million LLINs since 2004 (WHO, 2013a). While these investments have led to enormous scale up in population access to ITNs (Noor et al., 2009; Monasch et al., 2004), the target of universal coverage remains distant and millions of African households at risk remain unprotected (WHO, 2013a).

Bridging this gap is a key component of future strategies to reduce further the burden of malaria in Africa (WHO, 2014), and will require sustained commitment from donors, policy makers and national programmes. Central to these efforts is the capacity to monitor reliably current levels of ITN coverage in populations at risk and evaluate the systems that give rise to this coverage. This, in turn, enables progress towards international goals to be tracked and opportunities for efficiency gains to be identified. Such information is essential for evaluating the existing commodity and financing shortfalls and assessing future requirements if the target of universal coverage is to be achieved.

Modelling coverage

To facilitate standardised and comparable monitoring of ITN coverage through time, WHO and the Roll Back Malaria Monitoring and Evaluation Reference Group (RBM-MERG) has over the past decade defined a series of indicators to capture two different aspects of ITN coverage: access and use. Gold standard measurements of these indicators are provided by nationally representative household surveys such as Demographic and Health Surveys (DHS) (Measure, 2014), Multiple Indicator Cluster Surveys (MICS) (UNICEF, 2012), and Malaria Indicator Surveys (MIS) (RBM, 2014a). These surveys are carried out relatively infrequently, however, meaning they cannot be used directly for evaluating year-on-year coverage trends or for generating timely estimates of continent-wide coverage levels. In contrast, programmatic data such as the number of ITNs delivered and distributed within countries, while not describing coverage directly, are available for most countries and years (WHO, 2013a ). In a 2009 study, Flaxman and colleagues (Flaxman et al., 2010) used a compartmental modelling approach to link these programmatic and survey data, generating annual estimates of the two ITN indicators recommended at that time on access (% households with at least one ITN) and use (% children < 5 years old who slept under an ITN the previous night).

Since that study, there has been increasing recognition that a richer set of indictors is required to identify the complex nature of ITN coverage (Kilian et al., 2013). An intra-household 'ownership gap' may exist whereby many households with some nets may not have enough for one net between two occupants (the recommended minimum level of protection (WHO, 2013b). Similarly, a 'usage gap' may exist whereby individuals with access to a net do not sleep under it. In response, the measurement of two additional indicators was recommended: % households with at least one ITN for every two people and % population with access to an ITN within their household (assuming each net was used by two people) (RBM, UNICEF, WHO, 2013; RBM, 2011). In addition, the indicator on usage was extended to include the entire population rather than only children under 5 years old. This updated set of four indicators, used individually and in combination, has the potential to provide a nuanced picture of ITN access and use patterns that can directly guide operational decision making (Kilian et al., 2013). To achieve this, there is a need to develop modelling frameworks to allow all four to be tracked through time.

Evaluating efficiency

Countries have an ongoing struggle to maintain high LLIN coverage in the face of continuous loss of nets from households due to damage, repurposing, or movement away from target areas. In response, systems need to be responsive to emerging coverage gaps by ensuring nets are distributed to households that need them and avoiding over-allocation (i.e. distribution of nets to those that already have them). Together, the rate of net loss and the degree of over-allocation of new nets play a key role in determining how efficiently delivery to countries will translate into household coverage levels. These factors are not currently well understood but triangulation of survey and programmatic data allows new insights into both.

Estimating future needs

The WHO define universal access to ITNs on the basis that two people can share one net. Using the working assumptions of a 3-year ITN lifespan and a 1.8 person-per-net ratio (one-between-two but allowing for odd-numbered households), a simple calculation yields an indicative estimate of 150 million new nets required each year to provide universal coverage to an African population at risk of around 810 million (WHO, 2013a). To support country planning and donor application processes (RBM-HWG, 2014), a more elaborate needs assessment approach has been developed by the RBM Harmonization Working Group (RBM-HWG) and implemented by 41 of the 47 endemic African countries (RBM, 2014; Paintain et al., 2013). The tool takes into account the size and structure of national target populations, a 1.8 person-per-net ratio for mass campaigns, additional routine distribution mechanisms employed by countries, and volumes of previously distributed nets and their likely rates of loss through time. Countries have used these inputs to calculate requirements for new nets to achieve national coverage targets, leading to an estimated continent-wide need for 920 million ITNs over the 2014–2017 period (approximately 230 million per year) (RBM, 2014). This tool provides a transparent, intuitive and standardised mechanism for comparing forecasted needs against current financing levels and identifying likely shortfalls. However, calculated needs are sensitive to assumptions about how a given volume of new nets will translate into population coverage, and inefficiencies in the system such as such as over-allocation and rate of net loss are not accounted for explicitly in the current needs assessment exercise.

The purpose of this study is to define a new dynamic modelling approach, triangulating all available data on ITN delivery, distribution and coverage in sub-Saharan Africa in order to (i) provide validated and data-driven time-series estimates for all four internationally recommended ITN indicators; (ii) explore and quantify different aspects of system efficiency and how these contribute to reduced coverage levels; and (iii) estimate future LLIN needs to achieve universal access by 2017 under different efficiency scenarios and how these compare to existing needs assessment estimates.

Results

Net stock estimates

Figure 1A summarises the main inputs to and outputs from the stock-and-flow model for LLINs when aggregated at the continental level. Some 718 million LLINs have been delivered across the 40 endemic countries since their introduction in 2004. As is well documented (WHO, 2013a), annual LLIN deliveries increased year-on-year from 2004 to 2010, reaching 145 million in that year, but then declined dramatically in 2011 and 2012 to less than half that amount before rising again to 143 million in 2013 (green line). Taking into account rates of loss in households, these LLIN deliveries led to a continental net crop shown by the red line. We estimate that there were 252 million LLINs in sub-Saharan households by the end of 2013, with that net crop growing approximately linearly from 2004, with the exception of a slow-down resulting from the reduced supply of nets in 2011–2012. Figure 1B shows equivalent distribution and resulting net crop estimates for cITNs, which constituted nearly all ITNs prior to 2005 but diminished rapidly in importance following the introduction of LLINs thereafter.10.7554/eLife.09672.003

Figure 1.

Time series of ITN delivery, distribution, and estimated net crop in sub-Saharan households 2000–2013 for (A) LLINs and (B) cITNs. 

Manufacturer data on deliveries were available for LLINs only. cITNs, conventional insecticide-treated nets; HHs, households; ITNs, insecticide-treated nets; LLINs, long-lasting insecticidal nets; NMCP, National Malaria Control Programme.

DOI: http://dx.doi.org/10.7554/eLife.09672.003

Coverage estimates

Figure 2 shows continent-level time-series estimates of the four internationally recommended ITN indicators, along with the 'access gap' indicator. All four indicators show a similar temporal trend: very low coverage levels and modest year-on-year increases for the first 5 years from 2000, with a marked inflexion point in 2005 and much more rapid gains thereafter. Importantly, however, all four indicators show that the pace of increase has, overall, slowed since 2005. By the end of 2013, we estimate that around two-thirds (66%, 95% CI 62%–71%) of households at risk owned at least one ITN. However, less than one-third (31%, 29%–34%) owned enough for one ITN between two people. This much lower level of adequate ownership is reflected in the levels of access and use, with 48% (45%–51%) of people at risk having access to an ITN within their household (on a one-between-two basis) and 43% (39%–46%) sleeping under an ITN the previous night. Comparison of Figure 2A,B demonstrates that many households that own some ITNs do not own enough for one-between-two, and this is captured in the time-series for the 'ownership gap' (Figure 2E). Encouragingly, this gap has been narrowed from 77% (76%–78%) of net-owning households having insufficient nets in 2000 to 56% (54%–57%) in 2013. Analysis of the 'use gap' suggested a large majority (89%, 84%–93%) of those with access to an ITN in the household slept under it the previous night, and we found no evidence of significant change in this proportion through time.10.7554/eLife.09672.004

Figure 2.

Continental-level time series of estimated ITN coverage indicators for the years 2000–2013.

(A) % households with at least one ITN; (B) % households with at least one ITN for every two people; (C) % population with access to an ITN within their household; (D) % population who slept under an ITN the previous night; (E) 'ownership gap', the % of ITN-owning households with insufficient ITNs for one-between-two. Black circles are the annual estimates; pink envelopes denote the 95% posterior credible interval. ITNs, insecticide-treated nets.

DOI: http://dx.doi.org/10.7554/eLife.09672.004

The relatively smooth temporal trends seen at continental level obscure a great deal of complexity in the patterns of ITN scale-up occurring at national level (Figure 3). Nearly all countries began with very low coverage levels in 2000 and display a marked inflection point towards the middle of the decade, although there was considerable variation in the timing of onset of concerted scale-up activities. Importantly, the monotonic increases in coverage seen at the aggregated continental level are often replaced at national level with pronounced periods of rise and fall, and in many cases, 2013 does not represent the peak year. Variation in contemporary levels of coverage remains stark. The population with access to ITNs within the household, for example, was at or below 15% in seven countries in 2013, while above 70% for the top four.10.7554/eLife.09672.005

Figure 3.

Country-level time series of estimated ITN coverage indicators 2000–2013.

Each plot shows the four ITN coverage indicators: % households with at least one ITN (black); % households with at least one ITN for every two people (red); % population with access to an ITN within their household (green); % population who slept under an ITN the previous night (blue). CAR = Central African Republic; DRC = Democratic Republic of Congo; ITNs, insecticide-treated nets; HH = household.

DOI: http://dx.doi.org/10.7554/eLife.09672.005

Over-allocation

Over the 14-year period since 2000, on average 15% (12%–18%) of all ITNs distributed to households were over-allocated (owned by households already owning sufficient nets for one-between-two). Figure 4 illustrates how these over-allocation rates have changed through time. Around 7% (6%–9%) of ITNs were over-allocated in 2000, and this has risen steadily to 27% (22%–32%) in 2013. The year-on-year increase in over-allocation is to some extent an expected consequence of the overall growth in ITN provision: we found that over-allocation increased approximately 15 percentage points for each one-ITN-per-capita increase in net crop. Over-allocation also varied substantially between countries, for example ranging in 2013 from 50% (36%–65%) in the Republic of the Congo to 11% (9%–15%) in Côte D’Ivoire.10.7554/eLife.09672.006

Figure 4.

Time series of over-allocation for the combined set of 40 sub-Saharan endemic countries, 2000–2013.

Over-allocation refers to insecticide-treated nets distributed to households already owning enough nets for one-between-two, measured as the percentage of over-allocated nets among all nets in households.

DOI: http://dx.doi.org/10.7554/eLife.09672.006

Net loss

Averaged over all years and all countries, we found the median retention time for LLINs in households was 23 (20–28) months. We found no statistically significant evidence of continent-wide temporal trends in retention times, but substantial between-country variation. Figure 5 plots the LLIN loss function representing the most recent three years (2011–2013) for each country individually (blue lines), along with the aggregated continental-level curve (red line). For reference, we also overlay on Figure 5 some alternative loss functions that have been proposed. Flaxman et al. (orange line) fitted very small annual loss rates (5%) for years 1, 2 and 3 - with all LLINs then assumed lost after 3 years (Flaxman et al., 2010). The RBM-HWG proposed rate of loss (green line) is 8, 20 and 50% of LLINs to remain after 1, 2 and 3 years, respectively, with all nets being lost thereafter (Networks, 2014). As can be seen, we found rates of loss for the first 3 years to be greater than both these alternatives for all countries. Both alternatives impose a three-year maximum retention time and our decision not to do so meant that we modelled a small proportion of LLINs lasting some years beyond that point.10.7554/eLife.09672.007

Figure 5.

Insecticide treated netretention.

Estimated long-lasting insecticidal net retention curves for each country individually (blue lines) and combined (red line), in both cases relating to the average of the most recent 3 years, 2011–2013. Also shown for reference are the rate of loss recommended in the Roll Back Malaria Harmonization Working Group needs assessment exercise (green line) and the loss rate fitted by Flaxman et al. (orange line).

DOI: http://dx.doi.org/10.7554/eLife.09672.007

ITN requirements to achieve universal coverage

Figure 6 shows the projected levels of coverage that we estimate would be achieved by the end of 2017 with LLIN deliveries for the 2014–2017 period varying from zero to 2.5 billion and under a range of different efficiency scenarios. The most important characteristic of our results is the pronounced shallowing of the delivery-coverage curves: proportionately smaller gains are made in coverage as more LLINs are delivered in an archetypal 'law of diminishing marginal returns'. This means that under a business-as-usual scenario, where current levels of over-allocation and LLIN loss persist, very large increases in LLIN delivery would be required to achieve high coverage. Under this scenario, we estimate that 1 billion LLINs (i.e. an average of 250 million per year) would be required to achieve 80% of the population with access to an LLIN in the household by the end of 2017, although this would only translate into 70% population use.10.7554/eLife.09672.008

Figure 6.

Projected 2017 coverage for sub-Saharan Africa in relation to number of LLINs delivered over 2014–2017 period.

(A) % households owning at least one ITN; (B) % households owning enough ITN for one between two; (C) % population with access to ITN within the household; (D) % population sleeping under an ITN the previous night; (E) 'ownership gap', the % of ITN-owning households with insufficient ITNs for one-between-two. For each indicator, we project likely coverage under four scenarios: current levels of over-allocation and net loss (i.e. 'business as usual'); with minimised over-allocation; with longer average net retention (3-yr median); and with both minimised over-allocation and longer net retention. The vertical dashed lines indicate the number of LLINs calculated as required over the period under the country programmatic needs assessment supported by Roll Back Malaria Harmonization Working Group. LLINs, long-lasting insecticidal nets; ITNs, insecticide-treated nets.

DOI: http://dx.doi.org/10.7554/eLife.09672.008

The extent to which coverage gains diminish as deliveries increase is mitigated substantially when over-allocation and ITN loss rate are reduced. In a scenario with minimised over-allocation (where over allocation is set to zero), 80% population access in 2017 would be achievable with just 700 million nets (175 million per year). Reducing ITN loss rate to a 3-year median retention time would have a broadly similar impact, acting in isolation, to minimising over-allocation. If these two hypothetical efficiency gains were combined, however, 80% access could be reached in 2017 with around 560 million nets (140 million per year). We found that the relative importance of the over-allocation and LLIN loss rates changed as more LLINs were introduced. Increasing LLIN retention times was the most important factor at low levels of net delivery, but as more and more nets were provided, over-allocation became progressively more important. This is intuitive since it becomes increasingly difficult to avoid over-allocation as more households obtain adequate numbers of nets.

For reference, we also plot on Figure 6 the 920 million additional LLINs calculated by countries as required for universal coverage of targeted populations by 2017 under the RBM-HWG needs assessment exercise. Under current levels of over-allocation and net loss, we estimate that by the end of 2017 this quantity of new LLINs would translate into 77% access (among those populations targeted by countries for ITN coverage) and, assuming current behaviour patterns continue, 68% sleeping under an ITN. Under the combined efficiency scenario with minimised over-allocation and 3-yr median ITN retention time, however, the 920 million nets would approach universal access (slightly over 95%).

Discussion

By linking manufacturer, programme and national survey data using a conceptually simple model framework, the intention has been to provide a transparent and intuitive mechanism for tracking net crops and resulting household coverage that reflects the input data while simultaneously providing a range of insights about the system itself. In doing so we have been able to (i) provide a new approach for estimating past trends and contemporary levels of ITN coverage; (ii) explore the effects of uneven net distribution between households and the rates of net loss once in households; and (iii) use these insights to estimate how many LLINs are likely to be required to achieve different coverage targets in sub-Saharan Africa.

We have, for the first time, extended dynamic model-derived estimation of ITN coverage to all four internationally recognized indicators, along with the two 'gap' metrics. Our results reinforce a simple message: while gains in ITN coverage have been impressive, there remains an enormous challenge if the goal of universal access is to be achieved and sustained. The importance of the new expanded suite of indicators is also exemplified: while an encouraging two-thirds of households now own at least one ITN, less than half of these have enough to protect everyone who lives there. This ownership gap is narrowing but the disparity remains evident across nearly all countries. Conversely, there is little evidence that non-use of available nets contributes substantially to low coverage levels. We therefore reinforce earlier studies that suggest the overwhelming barrier to not sleeping under an ITN is lack of access rather than lack of use WHO, 2013a; Eisele et al., 2009; 2011; Koenker and Kilian, 2014; Koenker et al., 2014). Of course, non-use may be important in certain local contexts, and finer-scale analysis can support identification of areas where behaviour change communication interventions may be appropriate to reduce it (Kilian et al., 2013).

We found substantial over-allocation of nets to households already owning a sufficient quantity, and that this became more pronounced as overall ownership levels increased through time. Mass distribution campaigns can, in principle, be designed to minimise over-allocation and maximise evenness of nets allocated to households strictly on the basis of households members and pre-existing nets. As other studies have highlighted, however, any possible commodity savings achieved by such strategies must be compared against the operational cost of these more complex distribution mechanisms (Yukich et al., 2013). What is certain is that over-allocation becomes a major barrier to achieving universal coverage when levels of ITN provision are high because most new incoming nets are simply leading to surpluses in many households, while elsewhere there remains a shortfall. This may have a disproportionately high public health impact if those surplus nets are concentrated in households at lowest risk. Wealthier, better educated and more urban households may be better placed to obtain available nets but are often located in regions of lower transmission (Steketee and Eisele, 2009; Webster et al., 2005). While beyond the scope of the present study, the approaches we have developed here could be extended to consider these issues of equity in coverage versus risk in more detail.

One of the most important observations in our study is that LLINs may be lost from households at a substantially faster rate than is currently assumed. Importantly, we assess loss by comparing total inputs to countries (from deliveries) to total numbers in households (net crop), and so we measure real losses rather than, for example, reallocation of nets between relatives (Koenker et al., 2014). Longer retention times of the sort observed in some local studies are not supported by the body of evidence we have provided by triangulating large-scale net distributions and household survey data. This more rapid loss rate has potentially important implications for existing guidelines. Current RBM guidance is for mass ITN campaigns to be conducted every 3 years, complemented by continuous distribution of nets via routine channels in order to maintain coverage levels between those campaigns. However, whatever levels of coverage are achieved by a given campaign, we estimate that one-half of the campaign nets distributed, on average, will not be present in households just 2 years later. Our coverage time-series for many countries suggest that routine distribution channels are not yet compensating fully for this rate of loss, often displaying pronounced dips in coverage levels between mass campaigns. Maintaining higher continuous coverage therefore clearly requires some combination of more frequent campaigns, greater ongoing distribution between campaigns, or more durable nets and improved care behaviour by users that lead to longer overall retention times.

We considered nets in households as simply present or absent, with no allowance for their condition. In reality, of course, nets may be retained by households (and thus 'present' in our calculations) even when they are badly torn, or have diminished insecticidal properties. As such, our estimates of 'coverage' would be revised downwards if additional measures of net efficacy were included. Our model is able to provide an estimate for every country and every year of the age-profile of ITNs in households. This raises the possibility of extending the predictions to incorporate modelled or observational data on average rates of net degradation in different contexts (Briët et al., 2012) to explore measures of entomologically effective coverage.

Tools developed to assist countries to calculate LLIN requirements, have tended to define need using a simple ratio to populations at risk (such as 1.8 people per net), and have made allowances for net loss from households using pre-defined rates of loss. We have been able to show that true LLIN requirements are likely to be considerably larger when the more rapid rates of loss are taken into account, along with the additional effect of likely over-allocation patterns. This more realistic framework not only provides the basis for more accurate needs assessments but identifies the relative importance of these different factors in determining the coverage that can be achieved for a given delivery level. Our analysis of future LLIN needs from the present time to 2017 demonstrates how these factors lead to a pronounced law of diminishing returns: as more nets are introduced to a population, proportional increases in coverage diminish, with over-allocation a particular problem at high net provision levels.

Under business-as-usual, the number of nets required to approach full coverage is prohibitively large. Clearly, however, reducing current system inefficiencies and increasing net retention are not straightforward and already the subject of much attention by countries and international partners. Over-allocation is the complex result of different distribution strategies and varying levels of population access to services, and any solution comes with its own cost. Net retention can doubtless be increased by improved LLIN technology coupled with behaviour-change communication efforts, although it is also feasible that retention times may reduce when overall net provision increases (with new nets displacing older ones). Additionally, we look only at the RBM definition of use and ignore the effectiveness of nets in repelling mosquitoes once they are being used. This is potentially an important confounder when considering retention times. While not aiming to provide solutions to these complex challenges, the results we present here provide an analytical framework in which the impact of theoretical efficiency gains can be assessed and this could be extended to include formal cost–effectiveness analysis.

In conclusion, our results provide evidence that LLIN requirements to achieve universal coverage have been underestimated. If obtaining higher coverage remains an accepted goal of the international community, then larger LLIN volumes must be considered and planned for at national and international levels. We emphasise, however, that this would be best achieved in parallel with a renewed focus on maximising the efficiency of coverage achieved for each new net financed. Given that the pattern of diminishing coverage returns for each dollar spent is likely to be unavoidable, the cost–effectiveness of pursuing universal coverage rather than a lower operational target must ultimately be weighed against alternative malaria control investments.

Materials and methods

Overview

Two important preceding studies have sought to model national-level ITN delivery, distribution, and coverage: the Flaxman et al. study (Flaxman et al., 2010) and the work of Albert Killian culminating in the NetCALC tool (Networks, 2014) and a series of related publications (Paintain et al., 2013; Yukich et al., 2013). Although very different in implementation, both approached the problem in a similar two-stage process. First, a mechanism was defined for estimating net crop — the total number of ITNs in households in a country at a given point in time—taking into account inputs to the system (e.g. deliveries of ITNs to a country) and outputs (e.g. the discard of worn ITNs from households). Second, empirical modelling was used to translate estimated net crops into resulting levels of coverage (e.g. access within households). We have adopted a similar analytical outline, but the models we have developed for each stage differ structurally and conceptually from these earlier efforts. Our underlying principle has been to represent the ITN system in a simple and intuitive way and to parameterise that system using a data-driven approach that minimises the reliance on assumptions or small external datasets. In this Methods section, we describe: (i) the main data sources used; (ii) a new compartmental model for estimating net crop that also offers insights into rates of ITN loss from households; (iii) a new coverage model linking net crop to household net access and use that also assesses the efficiency of between-household distribution (i.e. the extent of over-allocation); and (iv) the use of our models to predict future ITN requirements to meet the goal of universal access. A schematic overview of our analytical framework is provided in Figure 7, and additional methodological detail is provided in the Supplementary Information.10.7554/eLife.09672.009

Figure 7.

Schematic showing overall analytical framework linking data, model components, and outputs.

HH = household; ITN, insecticide-treated net; NMCP = National Malaria Control Programme.

DOI: http://dx.doi.org/10.7554/eLife.09672.009

Data

We used three principal sources of data to fit our models. These are described briefly below and in more detail in Supplementary Information.

LLINs delivered to countries: data provided to WHO by Milliner Global Associates on the number of LLINs delivered by approved manufacturers to each country each year (WHO, 2013a; AMP, 2014). These were complete for each country from 2000 to 2013 inclusive.

ITNs distributed within countries: data provided to WHO by National Malaria Control Programmes (NMCPs) on the number of cITN and LLINs distributed annually within each country (WHO, 2013a). Data were available for 365 of the 560 country-years addressed in the study. We treated these data as only partial records of distribution activities because the extent to which NMCP reporting captures distribution by non-government agencies is not known for all countries.

Nationally representative household surveys. We assembled 99 national surveys from 39 sub-Saharan African countries from 2001–2013, covering 18% of all possible country-years since 2000 (Figure 8). More recent surveys provided household-level data on the number of cITNs, LLINs, people within each dwelling, and people sleeping under nets the previous night. RBM-MERG guidelines detail the conversion of these data into the standardised ITN indicators (RBM, UNICEF, WHO, 2013) and, in combination with national population data (UNPD, 2012), they can yield an estimate of national net crop (see Supplementary Information). Older surveys had less information: providing data on use but not ownership, for example, or for cITNs but not LLINs (see Supplementary Information). For most surveys (95/99), we were able to access the underlying data, while for the remaining four we used only the survey report.

10.7554/eLife.09672.010

Figure 8.

Distribution of national survey data on ITN net crop and household ownership, access and use used in this study, by country and year.

The different types of survey are shown in the key: CAR = Central African Republic; DHS = Demographic and Health Survey; DRC = Democratic Republic of Congo; ITN, insecticide-treated net; MICS = Multiple Indicator Cluster Survey; MIS = Malaria Indicator Survey; STP = São Tomé and Príncipe.

DOI: http://dx.doi.org/10.7554/eLife.09672.010

Countries and populations at risk

Our main analysis covered 40 of the 47 (WHO, 2013a) malaria endemic countries of sub-Saharan Africa. We excluded six endemic countries on the basis that ITNs do not form an important part of their vector control programme, as reported by the respective NMCPs to the African Leaders Malaria Alliance, ALMA (M. Renshaw, pers. comm. 3rd August 2014). These were Botswana, Cape Verde, Namibia, São Tomé and Príncipe, South Africa and Swaziland. We also excluded the small island nation of Mayotte, for which no ITN delivery or distribution data were available. We limited all analyses to those populations categorized as being at risk by NMCPs (WHO, 2013a). When interpreting NMCP distribution and household ownership data, we made the simplifying assumption that all reported ITNs were distributed among, and owned within, households situated in malaria endemic regions (Burgert et al., 2012). Additionally, we used data from African Leaders Malaria Alliance (ALMA) on the proportion of populations at risk targeted for ITNs versus IRS, and downscaled targeted populations at risk accordingly. It should be noted that restricting the distribution of ITNs to populations at risk makes the assumption that no ITNs are distributed to populations not at risk.

Estimating national net crops through time

Like Flaxman et al.(Flaxman et al., 2010), we represented national ITN systems using a discrete time stock-and-flow model. In this structure, a series of compartments were defined that contained a given number of nets at each time-step, with possible movement of nets from one compartment to another between time-steps (see Supplementary Information). Nets delivered to a country by manufacturers were modelled as first entering a 'country stock' compartment (stored in-country but not yet distributed to households). Nets were then available from this stock for distribution to households by the NMCP or other distribution channels. Years where NMCP distributions were smaller than available country stock represented potential ‘under-distribution’, with nets left to stockpile rather than reaching households. However, because of the uncertainty associated with NMCP distribution data, these discrepancies could simply reflect under-reporting of distribution levels. To accommodate this uncertainty, we specified the number of nets distributed in a given year as a range, with all available country stock as one extreme (the maximum nets that could be delivered) and the NMCP-reported value (the assumed minimum distribution level) as the other.

New nets reaching households joined older nets remaining from earlier time-steps to constitute the total household net crop, with the duration of net retention by households described by a loss function. In this representation, the net crop simply reflected the differences over time between inputs to and outputs from households. This meant that distribution, net crop, and the loss function together formed a closed system: the three must triangulate exactly and knowledge of any two components allowed the third to be calculated directly. Flaxman et al. (Flaxman et al., 2010) assembled data from six studies on ITN durability and rates of loss. Using a loss function fitted to these data, however, they found that the three components tended not to triangulate: net crops observed in surveys were too small, given the data on nets distributed to households and their modelled rate of loss. Their interpretation was that the number of ITNs distributed each year may be systematically over-reported by NMCPs, and a 'bias parameter' was included in the model, adjusting downward the volume of nets entering households in each country compared with reported levels. As described above, we took a different approach: with no a priori expectation that NMCP distribution reports exaggerate distribution levels. Rather than fitting the loss function to a small external dataset, we fitted this function directly to the distribution and net crop data within the stock-and-flow model itself. Conceptually, this reflected the view that the 560 country-years of distribution data triangulated against the 102 survey-derived national net crop values represented a more impartial and data-driven way of inferring rates of loss than using limited data from local ITN retention studies. Loss functions were fitted on a country-by-country basis, allowed to vary through time, and defined separately for cITNs and LLINs. We compared these fitted loss functions to existing assumptions about rates of net loss from households. The stock-and-flow model was fitted using Bayesian inference and Markov chain Monte Carlo (MCMC), providing time-series estimates of national household net crop for cITNs and LLINs in each country along with evaluation of under-distribution, all with posterior credible intervals. A complete technical description is provided in the Supplementary Information.

Estimating national ITN access and use indicators from net crop

Levels of ITN access within households depend not only on the total number of ITNs in a country (i.e. net crop), but on how those nets are distributed between households. In simple terms, a more even distribution yields a greater proportion of households owning nets than if those same nets are concentrated in fewer households. Many recent national surveys report the number of ITNs observed in each surveyed household. This allows, a histogram to be generated that summarises the net ownership pattern (i.e. the proportion of households with zero nets, one net, two nets and so on). By analysing such data from multiple surveys, previous studies have demonstrated that histograms for different countries vary in a broadly predictable way according to national net crop (Flaxman et al., 2010; Yukich et al., 2013). By representing these histograms using a formal statistical distribution (such as the negative binomial), and linking its parameters to net crop, predicted histograms can be generated for any country-year for which a net crop estimate is available (Flaxman et al., 2010; Yukich et al., 2013). These histograms, in turn, allow direct calculation of the first access coverage indicator (% households owning one or more ITN). We took the view that this approach—linking net crop to a statistical distribution, and using the distribution to calculate access indicators—is preferable to the alternative of regressing the access indicators against net crop directly. The latter approach, used in the NetCalc tool (Networks, 2014), is simpler but provides less direct insight into the patterns of between-household ITN distribution that ultimately link net crops to access levels.

One aspect that is known to strongly influence the relationship between net crop and household ownership distribution is the size of households found in different countries (Networks, 2014; Yukich et al., 2013), which varies greatly across sub-Saharan Africa (Swaziland, for example has an average household size of around three members, while in Senegal the average is nearly ten). Household size also, of course, determines whether a given number of owned nets will be sufficient to provide access to all residents. We extended earlier analyses (Flaxman et al., 2010; Yukich et al., 2013) to explicitly account for household size: using a bivariate (i.e. two- rather than one-dimensional) histogram model to link net crop to ownership distributions for each household size stratum (see Supplementary Information). We replaced the negative binomial distribution with a 2-d zero-truncated Poisson distribution and, for each household size stratum, fitted the distribution using two parameters: (i) the proportion of households with zero ITNs and (ii) the mean number of ITNs per ITN-owning household. Using the household-level data from 83 national surveys, we found that both parameters were strongly related to national net crop, allowing bivariate histograms to be generated for every country-year that were closely representative of the true ITN ownership distribution.

Stratifying our analysis by household size had three important advantages over earlier approaches. First, the distribution of net ownership tended to vary substantially between households of different sizes within a given country and this variation would be missed if all households were considered together. Accounting for this enabled better fits to the data. This makes sense: all else being equal, larger households would be expected to own more nets than smaller ones and so distribution patterns would differ systematically. Second, the bivariate ownership histograms predicted for each country-year could be used to directly calculate all three indicators of household access. While a simple univariate histogram allows calculation of % households with at least one ITN, a bivariate histogram means the number of both ITNs and people in every household can be triangulated which, in turn, allows direct calculation of the two additional indicators: % households with at least one ITN for every two people and % population with access to an ITN within their household, along with the 'ownership gap' (see Supplementary Information). Linking these bivariate histograms to our annual net crop estimates for each country meant we could predict time-series of the access indicators at the national level from 2000–2013, with all parameters fitted in a Bayesian framework providing posterior credible intervals around each time-series. We also combined the country-level results to generate a set of continent-level indicator time-series, representing overall coverage levels among populations at risk in the 40 endemic countries. Third, the bivariate histograms allowed analysis of over-allocation: certain cells of the histogram represented households owning more ITNs than were required to achieve access on a one-between-two basis, and the proportion of the total net crop falling in this category was examined through time for every country.

We took a different approach for the final indicator, % population who slept under an ITN the previous night. ITN use is less directly linked to national net crop and is primarily determined by the availability of nets within households (Eisele et al., 2009). A total of 83 of the 102 national surveys contained data allowing the relationship to be explored between ITN use and each of the three access indicators with, perhaps unsurprisingly, % population with access to an ITN within their household displaying the largest correlation (adjusted R²= 0.96). We fitted this relationship across the 83 surveys using a simple Bayesian regression model (see Supplementary Information) and used it to predict time-series of the ITN use indicator for every country. The ratio of population use to access revealed the 'usage gap'—the fraction of the population with access to ITNs not using them—and between-country variation in this ratio was also explored.

Estimating ITN requirements to achieve universal access

Our two-stage modelling framework represented the pathway from ITN delivery into countries through to resulting levels of net access and use in households. It also accounted for two potential factors that act to reduce access levels, and allowed these to be quantified through time for each country. Using this architecture, it was possible to simulate delivery of any hypothetical volume of ITNs to a given country over a given future time period, to predict the levels of access and use that would result, and to examine the impact of different amounts of over-allocation and net loss. The current needs assessment exercise that countries are undertaking (RBM-HWG, 2014; RBM, 2014) is designed to identify the number of LLINs required to achieve coverage targets by 2017. We used our model to estimate the levels of access likely to be achieved if these forecast LLIN commodity needs were met across the 2014–2017 period under a 'business as usual' scenario, that is, with current levels of over-allocation and net loss, and compared these predicted levels with the objective of universal access among target populations. We then generalized this experiment to predict the likely level of coverage (for all four indicators) achievable by 2017 under a broad spectrum of LLIN delivery levels, equivalent to a total for sub-Saharan Africa (two of the 40 endemic countries in our study did not participate in the RBM-HWG needs assessment exercise [Djibouti and Equatorial Guinea], and so our scenario analysis is based on the set of 38 remaining countries; to maintain comparability through time, we combined needs assessment data for mainland Tanzania and Zanzibar, and for Sudan and South Sudan) of between zero and 2.5 billion nets across the 4-year period. Further, we ran these simulations under four scenarios: (i) 'business-as-usual' (where current levels of over-allocation and net loss were maintained); (ii) with no over-allocation (new LLINs are distributed preferentially to those households with zero LLINs, then to those with less than one-between-two); (iii) with reduced LLIN net loss by households (using a modelled 3-year median retention time); and (iv) with both no over-allocation and a 3-year median retention time.