Distribution of malaria exposure in endemic countries in Africa considering country levels of effective treatment

National levels of prevalence were taken from the prevalence surfaces estimated by the Malaria Atlas Project (MAP) for Plasmodium falciparium 2010 [7]. Estimates of prevalence in children aged 2 up to children before their 10th birthday (PfPR_2–10) across a 5 km × 5 km grid were extracted as posterior distributions from a Markov Chain Monte Carlo (MCMC) calculated via a Bayesian geostatistical model using survey data. The primary estimates are of PfPR_2–10 are available from the MAP website [26] as posterior densities.

National levels of access to effective malaria treatment were collated previously [25] and are detailed in Table 2. Effective malaria treatment is treatment that results in parasitological cure. In this work effective treatment are estimates of the probability, E ₁₄, that effective malaria treatment will be obtained during any 14-day period in which a fever occurs. Estimates were assembled at country level taking into account multiple factors for effectiveness of malaria case management, including probably of treatment-seeking, of type of care provider, of systems compliance with the recommended anti-malarial treatment, of adherence with the drug regimen, and the quality of the anti-malarial medications.

Two different methods were used to estimate distributions of malaria exposure (as measured by the entomological inoculation rate, EIR) from PfPR_2–10 data:

The prevalence-EIR relationships from method A and B were used to estimate a distribution of EIR for each country from the prevalence surfaces estimated by the MAP for 2010 [7]. Prevalence from the MCMC chains are weighted by each pixel-level value of population, and the percentiles of the distributions obtained by summarizing the whole set of MCMC chains. Corresponding to the PfPR_2–10 value for pixel j, from MAP, and MCMC iteration i, an EIR estimate, x _j ⁽ⁱ⁾ , is obtained. For method B this is

The corresponding estimate of the distribution of EIR over the whole country (including non-endemic areas, with EIR = 0) is obtained by binning x _j ⁽ⁱ⁾ into a limited number, K, of ranges \(X_{ 1} ,X_{ 2} , \ldots ,X_{K}\), and population weighting. Aggregating the estimates from the whole set of T sampled values of p _j ⁽ⁱ⁾ from the MCMC chains, each range is assigned probability:and I(x _j ⁽ⁱ⁾  ∊ X _k ) is an indicator taking value 1 if x _j ⁽ⁱ⁾ is in range X _k and zero otherwise. Here N _j is the population assigned to the pixel as determined by the gridded population of the world [29, 30]. For computational convenience we carried out the summation over i before summing over j.

The resulting distributions describe the proportion of each country’s population that one would expect to be living at a given level of prevalence. In many of the countries analysed, a proportion of the gridded population from [30] falls outside the boundary of the area defined by MAP as being within the spatial limits of endemic malaria transmission [7]. This proportion of the population was assigned an EIR of zero.

Two different estimates of the transmission distribution per geographic area were calculated by estimation method B, to examine sensitivity to the estimated level of access to effective treatment. To capture the situation before recent scale-up of artemisinin combination treatment (ACT), a common value of access to effective treatment for all countries was used assumed and at a value previously used in OpenMalaria simulations [31]. This value equates to approximately 15 % of all malaria cases receiving treatment resulting in parasitological cure. In addition, analyses were conducted using country-specific estimates of access to effective treatment [25]. Country levels of coverage of effective treatment are listed Table 2 and illustrated by map in Additional file 2: Figure S1 and in Fig. 3b.

National level estimates of the incidence of clinical malaria were projected from the EIR distributions derived from Method A and Method B using OpenMalaria simulations. These incorporate dynamic models of clinical incidence and treatment parameterized with Senegalese and Tanzanian data [23, 31] and models for severe disease and mortality [22], and hence provide clinical incidence estimates as an extension of EIR estimation (process illustrated in Fig. 3d). Separate estimates were made using the EIR estimates with Method A, those from with Method B with E₁₄ = 0.15, and those made with Method B with country specific E₁₄ values.

Estimated burden, via clinical incidence, derived by both methods was compared with those national level estimates of clinical malaria from the WMR. For most sub-Saharan African countries, these use a standard empirical relationship between clinical incidence and endemicity. Clinical incidence values were assigned to each endemicity level based on estimates of the numbers of events recorded in longitudinal surveys of febrile malaria episodes in children, detected either actively or passively [32‐34], established independently of effects of treatment rates [12]. For countries with low endemicity, WMR uses national surveillance data to estimate burden, with adjustments to allow for incomplete reporting.

National levels of PfPR_2–10 aggregated at country level after extracting from MAP [7] posterior distributions at each 5 by 5 km pixel illustrate high average levels of PfPR_2–10 in 2010 in many African countries but for many countries also the wide distribution of prevalence levels (values summarized in Table 4 and Additional file 1: Table S3 and shown as distributions in Additional file 2: Figure S2). Regional differences, local variation, and uncertainty within areas all contribute differently to the overall distributions, with the average levels of transmission highest in West and Central Africa. Much of Namibia, Botswana, and South Africa, and also several Sahelian countries are malaria free, as are highland areas of East Africa. Some of the variation is also a result of differences in the extent of recent intervention programmes. In some countries, intervention programmes have had little impact on 2010 prevalence (e.g. Benin, Burkina Faso, Côte d’Ivoire), while elsewhere prevalence has been considerably reduced in the last decade (e.g. Senegal, Tanzania, Zambia), or much of the population lives in areas on the margins of stable transmission (Somalia, North Sudan). The location of some major urban centres such as Nairobi and Lusaka at relatively high altitudes, with low transmission, strongly influences some of these profiles.

Where PfPR_2–10 is high, the OpenMalaria models predict on average a slightly higher EIR at a given prevalence than does the empirical model (method A), with relatively little influence of effective treatment (E ₁₄) (Fig. 2a, b). The fitted prevalence to EIR relationships for Method B are shown in Fig. 2b (model variant R133) and Additional file 2: Figure S3 (all 6 model variants). The six model variants all predict broadly similar, but nevertheless distinct, prevalence-EIR relationships. The general pattern for Method A is for prevalence to increase steeply with EIR at low transmission levels, but to saturate at higher transmission (Fig. 2a). The considerable variation around the best fitting curve for Method A, after adjusting for the different EIR measurement techniques used, is treated as random variation that contributes to uncertainty in the estimate of EIR from prevalence. This analysis does not allow for variations in the coverage or effectiveness of case management in the different studies, however such variation could account for much of this unexplained dispersion (compare with Fig. 2b). At lower transmission levels the fitted curves for Method B (OpenMalaria) vary considerably with E ₁₄, suggesting that effectiveness of case management is a particularly important driver of prevalence in such settings, with Method B estimating lower EIR at a given prevalence than the empirical model unless E ₁₄ is high (Fig. 2b). This is partly because Method B constrains estimated EIR to be zero at zero prevalence, while the empirically-based Method A does not capture or force this constraint.

The differences between the two relationships for prevalence and EIR are reflected in the estimated distributions of EIR by county (Fig. 4; Additional file 2: Figure S4). The EIR distributions are generally much more highly skewed than are the prevalence distributions. The distributions obtained with the empirical model (Method A: Fig. 4; Table 4 and Additional file 1: Table S4) and with the simulation models (Method B) that assume \(E_{14} = 0.15\) (Table 4 and Additional file 1: Table S5) are similar to each other for most countries, though the estimated median EIRs are generally somewhat higher for the estimates from the simulation models (Fig. 5). Where effectiveness of case management is high, the country specific assumptions for system effectiveness make substantial differences to the estimated EIR distributions (Fig. 4; Table 2; Additional file 2: Figure S2). In these countries, notably Zambia, Tanzania, São Tomé and Principe, the EIR distribution shifts to the right when the country-specific value of \({\text{E}}_{14}\) is used, reflecting lower prevalence than in a situation with the same EIR pattern, but less effective case management. The estimate of median EIR for these countries is thus much higher when country-specific effectiveness is considered. Conversely, in a few countries, where median prevalence is low, and case management is also poor, the estimated EIR distribution allowing for country-specific effectiveness is shifted slightly to the left (e.g. both South and North Sudan).

The EIR distributions are highly skewed, so that the arithmetic means are much higher than the medians (Figs. 4, 5). Except in some cases where prevalence is very low, the average EIR is higher when there is allowance for treatment (Method B), with a much larger shift in the mean than in the median of the distribution. When country specific E ₁₄ values are used (which are mostly higher than the 15 % shown in yellow), this makes little difference to the mean EIR, but substantial differences to the medians, reflecting the stronger relationship between treatment rates and prevalence when EIR is low, than when EIR is high.

The OpenMalaria simulations predict that steady state clinical incidence (over all ages) increases linearly with EIR in low transmission settings, tending to plateau at high EIR (with a suggestion, driven by the specific Senegalese data used to parameterize the models for older children and adults [35] that there may be a maximum in the curve at high prevalence). The initial slope is greater when \(E_{14}\) is higher, but the plateau occurs at a similar level of incidence irrespective of effective treatment level. These patterns are a consequence of the age-specific relationships between incidence and EIR shown in Fig. 6.

When these models are used to infer country-specific incidence of clinical malaria, there is a clear increase in incidence with average prevalence at the country level (Fig. 7), and no plateau is reached because even the countries with highest average transmission have only small populations in the very high EIR categories (Table 4 and Additional file 1: Table S2). The relationships between country-level EIR and estimated clinical malaria incidence are similar, irrespective of whether the EIR is estimated by Method A or Method B. Similarly, Method B estimates similar relationships between country-level EIR and clinical malaria incidence, irrespective of whether a common value, or a country specific estimate is used for the effectiveness of case management.

Country-specific estimates of clinical incidence using country EIR distributions is compared to published malaria cases from the World Malaria Report [14] (Fig. 8; Additional file 2: Figure S5). In general, projections of incidence using EIR derived from method B produces higher predictions than using EIR from method A, but in both cases the simulation models predict substantially more episodes of malaria than the cases reported in the World Malaria Report 2013 (Fig. 8a). There is also a much less steep relationship between the incidence rate and the overall burden (Fig. 8b). This can be explained by the empirical relationships between prevalence and case incidence used by WMR [12], which refer back to field research carried out prior to the widespread use of ACT [33, 36], and therefore do not allow for level of treatment. Moreover, only clinical episodes in children under 5 years of age are considered. The effect of high levels of treatment on reducing prevalence leads to much higher ratios of case-incidence to prevalence ratio than it would be without treatment (Fig. 7). OpenMalaria correctly predicts that in low transmission countries the majority of the clinical burden is in older age groups (Fig. 6). The difference between the methods is particularly evident for low-burden countries Namibia and Botswana, for which very low case numbers are reported by the WMR, with estimates based on adjustments to surveillance data.