Study area

Tanzania and its islands in the Indian Ocean (Fig 1A), located on the east coast of Africa and occupying 886,100 km² [16], are included in the study area. Its population is increasing (Fig 1B), reaching approximately 45 million in 2012 [17] and 48.8 million in 2015 [16]. The country remains one of the lowest income countries in the world, with a 2015 GDP per capita of approximately $879 U.S., equivalent to 8.7% of the world’s average [18]. The country has a tropical climate with wet and dry seasons that vary with its topography. The population distribution is extremely uneven. Nearly 80% of the population lives in low densities in arid rural areas while the remaining population occupies high-density urban areas including Dar es Salaam, with some areas of the city reaching over 3,133 people per km² [19].

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Fig 1. Map of the United Republic of Tanzania, human population density map, and Anopheles habitat suitability map.

The figure shows (A) an elevation map with major cities of Tanzania and neighbouring countries. The inset map details Tanzania’s location in eastern Africa. (B) Map of human population density from LandScan (http://web.ornl.gov/sci/landscan/) with ~1 km² (30 arc second) resolution. (C) The Maxent output map of relative Anopheles mosquito habitat suitability. The map ranges from blue to red representing low to high habitat suitability, respectively.

https://doi.org/10.1371/journal.pone.0205270.g001

In 2016, 100% of Tanzanians on both the mainland and Zanzibar region were at risk of malaria [9, 10]. The most dangerous malaria parasite, Plasmodium falciparum, is responsible for >85% of malaria cases in Tanzania, with pregnant women and children under the age of five at the highest risk [20]. Over 26% of all outpatient attendances are due to malaria infection, with an estimated 7.7 million confirmed malaria cases annually [9]. ITN distributions prioritize pregnant women and children under the age of five [7] while IRS applications mainly target malaria epidemic-prone areas [7, 12, 13].

Entomological records and niche model

The Anopheles mosquito niche model, built using Maxent software [21], v.3.3.3k, and described in detail in [6], predicted relative habitat suitability of Anopheles mosquitoes across Tanzania (Fig 1C). The initiation of large-scale distributions of mosquito nets in 2004 [8] required that the niche model be built using Anopheles coordinates from 1999–2003. This time period provided a total of 56 geographically-unique coordinates for model building, which exceeds the minimum requirements (>5) for informative predictions of species distributions [22], though combinations of all records from 1935–2003 as well as 1935–2014 yielded qualitatively similar Maxent outputs. A database of over 400 published literature sources, supplemented with unpublished data collections and the online database IR Mapper [23] from 1935 to 2014 was used for georeferenced coordinates of Anopheles mosquitoes. Lack of geographically-unique species-level identifications for many of the georeferenced Anopheles records required all recorded Anopheles species within the 1999–2003 time period (i.e. mosquitoes recorded as A. arabiensis, A. gambiae s.s., A. gambiae s.l., and A. funestus) to be combined for model building.

Multiple models were constructed and tested for accuracy using elevation as well as land cover, human population distribution, and variations of annual temperature and normalized difference vegetation index (NDVI) for 2001 (average, minimum, and maximum). Using data provided by the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor on the Terra satellite, we collected all 8-day land surface temperature composites (MOD11A2, 1000-m resolution), all monthly NDVI composites (MOD11A3, 1000-m resolution), and land cover (MCD12Q1, 500-m resolution) for 2001. Elevation data at 90-m resolution were collected from the Shuttle Radar Topography Mission [24]. Human population distribution data for 2001 were provided by the OakRidges National Laboratory Landscan database at 30 arc second (or ~1 km) resolution [25].

To assess model accuracy, occurrence records were randomly partitioned into model training (75%) and model testing (25%), with ten replicates run for each model using tenfold cross-validation and a randomized partitioning of training and testing data in each run [6]. The raster maps of habitat suitability were then averaged to determine relative habitat suitability for each grid cell. Model accuracy was then determined using both a threshold-dependent binomial omission test as well as a threshold-independent receiver operating characteristic analysis (AUC) [21]. The binomial test of omission used a fixed threshold for habitat suitability values of 0.1, a threshold value commonly used in other studies [e.g. 26]. The omission error rate was 7.14% at the 0.1 threshold, and remained below 20% up to a threshold of 0.25 (n = 56) [6]. The internal accuracy of the model was also high for the threshold-independent analysis, with an AUC of 0.872 (where AUC values approaching 1 indicate perfect discrimination between suitable and unsuitable areas for the study species, while values near 0.5 indicate a performance no better than random) [21].

Given the set of Anopheles presence records and the values of the selected environmental variables across Tanzania, Maxent produced a predicted distribution of Anopheles mosquitoes across the country by finding the distribution of maximum entropy, constrained by the expectation that the mosquitoes’ distribution matches their empirical average over the sampled locations [21]. The resulting map used for this analysis consists of 1-km² pixels of relative Anopheles mosquito habitat probability, rather than presence-absence of the species, where each cell ranges from 0 (i.e. low relative habitat suitability) to 1 (i.e. high relative habitat suitability). The binomial test of omission was repeated, also with a set threshold of 0.1, to test the habitat suitability map against independently-collected georeferenced cases of Plasmodium falciparum across Tanzania from the Malaria Atlas Project (MAP) website [27]. Model predictions of anopheline mosquito habitat suitability corresponded strongly to MAP records both from 1985–2012 (omission rate = 0.1599 for 919 geographically-unique P. falciparum records) as well as to those specifically from the study period of 1999–2003 (omission rate = 0.1321 for 107 P. falciparum records). In addition to validation against malaria prevalence rates, this model has persistently low omission error rates of anopheline observations, including those from much later (i.e. 1985–2012) and uses relatively high resolution satellite remote sensing data to generate spatially detailed predictions. Based on the fixed threshold of 0.1, our model prediction of habitat suitability was qualitatively similar to the 2001 continuous surface of predicted P. falciparum parasite rates in 2–10 year olds by the MAP [27]. However, the MAP models are developed at the continental scale and may not always be able to provide sufficient detail for within-country and within-district control efforts. As a result, our relative habitat suitability map in particular, and our method of predicting baseline mosquito habitat suitability in general, could further improve targeting for anti-malaria interventions within countries and districts by providing a higher-resolution extension to the MAP outputs.

Malaria control survey data

Here, we use countrywide Tanzanian data from the AIDS Indicator Survey (AIS) for the 2011–2012 period and the standard DHS survey for the 2015–2016 period (with permission from the Demographic and Health Surveys (DHS) program). The 2011–2012 AIS fieldwork was conducted between December 2011 and May 2012 while the 2015–2016 DHS fieldwork was conducted between August 2015 and February 2016, implemented by Tanzania’s National Bureau of Statistics [13]. Data were used specifically from the Malaria Indicator Survey (MIS) component of the 2011–2012 AIS and 2015–2016 DHS surveys. The MIS measures malaria prevention and treatment outcomes and provides data on the household coverage of malaria interventions, including mosquito net ownership (see [6]), mosquito net use, and IRS activities, amongst others. DHS procedures and questionnaires were reviewed and approved by the ICF International Institutional Review Board. Survey details are provided in associated reports [12, 13].

Survey data are presented as georeferenced cluster points across Tanzania (i.e. points representing 17–22 nearby surveyed households). To protect respondent confidentiality, the DHS used set parameters to displace each point [28]. Points categorized as urban were displaced between 0–2 km and those categorized as rural were displaced between 0–5 km, with 1% (or every 100^th point) displaced between 0–10 km. Shifts in distance and direction were random. However, displacement of the points was restricted to within district (‘admin2’) levels for the 2011–2012 AIS and the 2015–2016 DHS surveys. Randomized cluster displacement could therefore cross local administrative boundaries, such as ward boundaries, but not cross DHS district boundaries.

Mosquito net use and indoor residual spraying layers

The 2011–2012 AIS survey included data on 10,040 households and the 2015–2016 DHS survey included data on 12,563 households. The GPS dataset from each survey provided by the DHS comprised of 583 and 608 georeferenced, randomly-displaced cluster points, respectively. For the 2011–2012 dataset, eleven clusters were deleted due to missing data, with 439 rural and 133 urban clusters, and a total of 9,846 households, remaining in the final layer. Of these households, 8,533 were located on the mainland and 1,313 were located in the Zanzibar region. For the 2015–2016 dataset, one cluster was deleted due to missing data, with 427 rural and 180 urban clusters, and a total of 12,544 households, remaining in the final layer. Of these households, 10,789 were located on the mainland and 1,755 were located in the Zanzibar region.

With these two survey data sets, two malaria intervention questions were analyzed: 1) Did at least one child under the age of five use a mosquito net in the house the night before the survey was conducted? and 2) Was the dwelling sprayed for mosquitoes in the 12 months prior to the survey? Mosquito nets are defined by the DHS as any mosquito net (treated or untreated), a factory-treated net that does not require further treatment (LLIN) or a net that has been soaked with insecticide within the past 12 months [12]. The question regarding mosquito net use only looked at households in the surveyed clusters that had at least one child under the age of five and analyzed children recorded in the survey as ‘de facto’ (i.e. slept in the house the night before the survey was conducted). Data regarding responses for each child in each household were taken from the Household Member Recode data set, while data regarding household responses for IRS were taken from the Household Recode data set. Binary responses were given for each variable, with “No” given a value of 0 and “Yes” given a value of 1.

Buffer zones were created in ArcGIS v.10.1 (ESRI 2012, Redlands, CA) for each survey cluster to account for the random relocation of cluster locations for confidentiality purposes. Since cluster points were randomly displaced between 0–2 km for urban locations and 0–5 km for rural locations, buffers with a radius of 2 km were created for urban clusters and buffers with a radius of 5 km were created for rural clusters. The random relocation of clusters was restricted by district boundaries (see S1 Fig for ‘admin2’ district boundaries for each survey), so buffers that crossed into an adjacent district were made more spatially precise by being clipped along the boundary. This processing resulted in 572 cluster polygons for the 2011–2012 survey and 607 cluster polygons for the 2015–2016 survey.

Statistical analyses

We related malaria intervention variables to a baseline relative mosquito habitat suitability map for Tanzania using R statistical software [29], v.3.0.2. The two malaria intervention layers for each survey, created in ArcGIS 10.1 and consisting of buffer zones around each cluster and clipped to ‘admin2’ district boundaries, as well as the relative habitat suitability map created in Maxent, were imported into R. R was used to calculate an average relative mosquito habitat suitability value for each unique buffer zone of 2- or 5-km radius (see S1 and S2 Files for steps in ArcGIS and R used for these processes).

Mixed effects logistic models allow analysis of multilevel (i.e. hierarchical) data with binary or ordinal outcomes, where the multilevel structure may introduce correlations among observations within a surveyed cluster (e.g. among households) or within a household (e.g. among individuals) [30]. A mixed effects model is more suitable for the multilevel data provided by the DHS than a traditional fixed effects model because it allows for analysis of the fixed effect while treating surveyed groups as a random sample from a broader population of those groups throughout Tanzania [30–32]. In this analysis, the fixed effect is relative mosquito habitat suitability and the random effects are clusters of households. Both survey questions had a binary outcome (“Yes” = 1, “No” = 0). Mixed effects logistic regression analyses were therefore conducted in R using the ‘lme4’ package to test whether relative Anopheles habitat suitability predicted mosquito net use by children under the age of five or IRS in the last 12 months. Each model regressed the log odds of the outcome probability on the relative mosquito habitat suitability to estimate the probability that the household answered “Yes” (i.e. 1), given the random effect.

For each question, Eq (1) was used for the mixed effects logistic regression model. This model contains one random effect and one fixed effect to compare whether the log odds of at least one child under the age of five using a mosquito net in the household the night before the survey, as well as whether the log odds of a dwelling being sprayed for mosquitoes within the last 12 months, were related to relative mosquito habitat suitability: (1) Variables are defined as the following: p_jk = P(Y_jk = 1), the probability that the jth household in the kth cluster answers “Yes” to either having at least one child under the age of five using a mosquito net the previous night or having been sprayed for mosquitoes in the last 12 months, β = the coefficient of the fixed effect, x_k = the continuous fixed effect variable (the averaged relative mosquito habitat suitability from the buffer zone around each cluster), μ = the intercept, γ_k = the random intercept representing the random effect of the kth cluster. The distribution of Y_jk is Bin(1, p_jk), where the mixed effects logistic regression model assumes a binomial distribution of the response variable. It is assumed that γ_k follows a normal distribution with a mean of 0 and variance σ². For mosquito net use, we also separately tested for the additional potential random effect of households nested within surveyed clusters to compare whether the log odds of a child under the age of five using a mosquito net within a household the previous night was related to relative habitat suitability.

For both equations, the fixed effect regression coefficient β is therefore the log odds ratio of a higher malaria control effort (i.e. higher usage of mosquito nets by children under the age of five, or spraying of dwellings) versus a lower usage when x_k increases by one unit (in the case of this analysis, this would be an increase by 1% in relative mosquito habitat suitability), controlling for the random effect(s) in the model. Results were calculated using log odds (or logits) as opposed to odds ratios or probabilities because the log odds scale is linearized, translating to a 1 unit increase in the predictor resulting in a coefficient unit increase in the outcome, regardless of the values of other predictors. Random effects were treated as nested for the analyses, as opposed to crossed, because each individual was only surveyed in one household (i.e. the individual was not surveyed in more than one household) and, likewise, each household was only surveyed in one cluster.

In addition to providing the associated p values for each model outcome, we also report the marginal R² and conditional R² value using the ‘MuMIn’ package in R. The marginal R² value has been proposed as being more appropriate for mixed effects models than the traditional R² value, because it expresses an estimated variance explained only by fixed factors while disregarding that explained by random factors [33]. The conditional R² value expresses an estimated variance explained by both the fixed and random factors. While information criteria are often used as comparison tools for mixed models (e.g. Akaike Information Criterion, Bayesian information criterion), they are used for comparing between models where they select a ‘better’ or ‘best’ model from a set of candidate models [34]. Information criteria therefore provide an estimate of relative fit of alternative models, and do not measure any sort of absolute model fit [33]. Marginal and conditional R², by contrast, are extremely useful for mixed models because they provide an absolute value for model fit.

For mosquito net use, responses were calculated from a total of 8,828 surveyed children under the age of five from 5,480 households in 572 clusters from the 2011–2012 surveys. Responses were calculated from a total of 10,398 children under the age of five in 6,709 households in 607 clusters from the 2015–2016 survey. For IRS use, responses from 9,730 households were used from the 2011–2012 survey and 12,469 households were used from the 2015–2016 survey.

Due to the intensive use of IRS in the Lake and Zanzibar regions of the country compared to mosquito net distributions (Fig 2) [12, 13], analyses of dwellings being sprayed for mosquitoes in the past 12 months were conducted both countrywide and separately for a focus region of high data collection regions near Lake Victoria and on Zanzibar. According to the AIS 2011–2012 and the DHS 2015–2016 surveys [12, 13], Kagera, Mara, and Mwanza are all part of the Lake region (Fig 2A), while Pemba Island and Unguja Island are considered part of the Zanzibar region (Fig 2B), and all were specified as having been targeted by IRS initiatives. The Geita region, also part of the Lake region, was one of four new regions that formed at the time of the 2011–2012 survey design and also appears to have some IRS coverage, though the Geita region was not specified in the AIS 2011–2012 survey report as receiving IRS attention. The clipped regions of (1) Kagera, (2) Geita, (3) Mara, (4) Mwanza, (5) Pemba, and (6) Unguja were therefore analyzed separately for both surveys. Mixed effects logistic regression relating dwelling spraying and relative mosquito habitat suitability were tested for each of these six separate regions, as well as for the combined Lake region (i.e. Kagera, Geita, Mara, Mwanza), the combined Zanzibar region (i.e. Pemba Island and Unguja Island combined), and the combined Lake and Zanzibar regions, for each survey.

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Fig 2. The (A) Lake and (B) Zanzibar regions, with their corresponding districts analyzed separately for dwelling spraying.

The georeferenced buffer zones showing random effects contributed by each cluster are from the 2011–2012 AIS survey and are overlaid on the mosquito habitat suitability map of Tanzania. Similar regional boundaries were applied to the analysis of the 2015–2016 DHS survey data.

https://doi.org/10.1371/journal.pone.0205270.g002

Since analyses of mosquito net use were not similarly restricted to specific regions, an additional analysis was conducted to test for any potential effects of undersampled districts on the countrywide models. The lowest ~10% of sampled districts were removed (i.e. all districts each containing only one sampled cluster of households) for each survey and the models were rerun. For the 2011–2012 survey comprising 148 districts, 14 districts and their associated data were deleted. For the 2015–2016 survey comprising 169 districts, 15 districts and their associated data were deleted.

To test model performance in controlling for spatial autocorrelation in residuals, we calculated Moran’s I for the residuals from each model, where a Moran’s I value of -1 indicates perfect dispersion, a value of +1 indicates perfect correlation, and a value of 0 indicates a random spatial pattern. In addition, given the mixed effects logistic regression approach used for our analysis, Moran’s I was also run on the random effect of the clusters. The random effects demonstrate the variation in malaria intervention use specific to each cluster from the model intercept. A negative random effect value means that the cluster was less likely to use the malaria intervention than the overall population when mosquito habitat suitability was held constant. Likewise, a positive random effect value means that the cluster was more likely to use the malaria intervention than the overall population when mosquito habitat suitability was held constant. Due to the targeted nature of IRS initiatives countrywide towards areas of higher malaria prevalence [14], these spatial autocorrelation tests were conducted both for the countrywide as well as the district- and region-wide analyses.

Countrywide results for all malaria intervention questions

At a national scale, analyses of the 2011–2012 AIS dataset yielded no significant results (p>0.05) for the log odds of households having at least one child under five using a mosquito net the night before the survey, in relation to relative mosquito habitat suitability (Table 1). For the 2015–2016 DHS dataset, there were statistically significant but very weak increases in the log odds of households having at least one child under five using a mosquito net the night before the survey (β = 1.466, 95% C.I. = 0.848–2.103, p < 0.001, marginal R² = 0.020, conditional R² = 0.452) towards areas of higher relative mosquito habitat suitability (Table 1). Separate models were run for mosquito net use to test for the additional potential random effect of households nested within each cluster. These models, comparing whether the log odds of a child under the age of five using a mosquito net the previous night was related to relative habitat suitability, yielded qualitatively similar results for each survey period. Model results after deletion of the lowest 10% of sampled districts for each survey also yielded qualitatively similar results. Analyses revealed significant and stronger increases in the log odds of dwellings being sprayed for mosquitoes within the last 12 months toward areas with higher predicted mosquito habitat suitability for both the 2011–2012 survey (β = 13.466, 95% C.I. = 10.488–16.456, p << 1x10^-6, marginal R² = 0.144, conditional R² = 0.952) and the 2015–2016 survey (β = 6.817, 95% C.I. = 5.439–8.303, p << 1x10^-6, marginal R² = 0.136, conditional R² = 0.804) (Table 1).

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Table 1. Results of the countrywide mixed effects logistic regression analyses.

https://doi.org/10.1371/journal.pone.0205270.t001

Spatial autocorrelation results were all statistically significant (p<0.001) but relatively low for both the model residuals and random effects of clusters across both surveys and questions (Moran’s I values ranged from 0.076–0.193, see Table 2). However, for IRS use in the 2011–2012 survey, some spatial clustering appeared to be unaccounted for by the model (Moran’s I of model residuals = 0.337, Moran’s I of random effects of clusters = 0.254) (Table 2). The random effects contributed by each cluster for each factor analyzed are shown in Fig 3.

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Fig 3. The random effect contributed by each cluster for the two malaria questions analyzed per survey.

Random effects are shown for (A) and (B) Did at least one child use a mosquito net in the house the night before the survey? and (C) and (D) Was the dwelling sprayed for mosquitoes in the 12 months prior to the survey? Panels (A) and (C) show random effects from the 2011–2012 AIS survey and panels (B) and (D) show random effects from the 2015–2016 DHS survey. The random effects demonstrate the variation of each cluster from the model’s intercept (i.e. a negative random effect value means that the cluster had lower log odds of using the malaria intervention than the overall population mean when mosquito habitat suitability is held constant. The opposite applies to a positive random effect).

https://doi.org/10.1371/journal.pone.0205270.g003

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Table 2. Moran’s I results for country-wide analyses.

Moran’s I analyses were conducted on both model residuals as well as the random effect values of the clusters.

https://doi.org/10.1371/journal.pone.0205270.t002

Individual and combined-region results for IRS applications

Within-region models relating intervention use to models of mosquito habitat suitability yielded a surprising range of positive and negative relationships. Mixed effects logistic regression analyses demonstrated that the log odds of spraying over the previous 12 month period actually decreased toward areas with higher mosquito habitat suitability in the Mwanza region for both the 2011–2012 survey (β = -18.429, 95% C.I. = -40.051 –-1.769, p = 0.036, marginal R² = 0.176, conditional R² = 0.771), the 2015–2016 survey (β = -21.215, 95% C.I. = -37.382 –-9.835, p = 0.001, marginal R² = 0.363, conditional R² = 0.631), and on Pemba Island in the 2015–2016 survey (β = -8.512, 95% C.I. = -15.675 –-1.582, p = 0.014, marginal R² = 0.046, conditional R² = 0.213) (see S1 Table). However, a statistically-significant increase in the log odds of dwellings being sprayed towards areas of higher mosquito habitat suitability was seen in the Lake region in the 2011–2012 survey (β = 20.108, 95% C.I. = 4.394–32.562, p = 0.006, marginal R² = 0.067, conditional R² = 0.865) and in the combined Lake and Zanzibar regions in both the 2011–2012 survey (β = 9.338, 95% C.I. = 7.400–11.521, p<<1x10^-6, marginal R² = 0.327, conditional R² = 0.823) and in the 2015–2016 survey (β = 3.878, 95% C.I. = 2.604–5.242, p<<1x10^-6, marginal R² = 0.115, conditional R² = 0.639) (see S1 Table).

Spatial autocorrelation analyses of within-region model residuals and random effects of clusters also yielded a surprising range of positive and negative values with varying degrees of spatial autocorrelation. Moran’s I values were greater in the 2011–2012 dataset than in the 2015–2016 dataset. For the 2011–2012 survey, spatial autocorrelation analyses of model residuals were statistically significant for the Geita, Mara, and Mwanza districts and suggested some clustering (Moran’s I = 0.319, 0.336, and 0.298, respectively, p<0.001), as well as for the Lake region (Moran’s I = 0.241) and the combined Lake and Zanzibar region (Moran’s I = 0.321) (see S2 Table). Moran’s I values of the random effects of clusters yielded similar results (see S2 Table).

In the 2015–2016 survey, however, Moran’s I measurements of spatial autocorrelation analyses were often statistically significant but relatively small. Spatial autocorrelation analyses of model residuals were statistically significant for Kagera and Unguja (Moran’s I = 0.172 and 0.115, respectively, p<0.05), as well as for the Lake, Zanzibar, and combined Lake and Zanzibar region (Moran’s I = 0.054, 0.102, and 0.106, respectively, p<0.001). Moran’s I values of the random effects of clusters were also mostly relatively low and statistically significant for all districts and regions except Geita (see S2 Table).