Modeling Malaria Incidence Associated with Environmental Risk Factors in Ethiopia using the Geographically Weighted Regression Model, 2015-2016

Background: In Ethiopia, still, malaria is killing and affecting a lot of people of any age group somewhere in the country at any time. However, due to limited research, little is known about the spatial patterns and correlated risk factors on the wards scale. Methods: In this research, we explored spatial patterns and evaluated related potential environmental risk factors in the distribution of malaria incidence in Ethiopia in 2015 and 2016. Hot Spot Analysis (Getis-Ord Gi* statistic) was used to assess the clustering patterns of the disease. The ordinary least square (OLS), geographically weighted regression (GWR), and semiparametric geographically weighted regression (s-GWR) models were compared to describe the spatial association of potential environmental risk factors with malaria incidence. Results: Our results revealed a heterogeneous and highly clustered distribution of malaria incidence in Ethiopia during the study period. The s-GWR model best explained the spatial correlation of potential risk factors with malaria incidence and was used to produce predictive maps. The GWR model revealed that the relationship between malaria incidence and elevation, temperature, precipitation, relative humidity, and normalized difference vegetation index (NDVI) varied signicantly among the wards. During the study period, the s-GWR model provided a similar conclusion, except in the case of NDVI in 2015, and elevation and temperature in 2016, which were found to have a global relationship with malaria incidence. Hence, precipitation and relative humidity exhibited a varying relationship with malaria incidence among the wards in both years. Conclusions: This nding could be used in the formulation and execution of evidence-based malaria control and management program to allocate scare resources locally at the wards level. Moreover, these study results provide a scientic basis for malaria researchers in the country.


Study area
Ethiopia is located in the eastern part of African content approximately 30 -150N latitude and 330 -480E, longitude. Its land and water coverage is 1,000,000 and 104,300 square kilometres, respectively (Hagose, 2017). The total population of the country is 83.7 million (Ethiopian et al., 2014).
Ethiopia is one of the most densely populated areas in the world. The topography of the land varies from lowland to mountainous landscapes. The elevation in the study area varies between 1290 and 3000 meters above sea level (Fazzini, Bisci and Billi, 2015).
The study area map uses the World Geodetic System (WGS84) map projection as its reference coordinate system for data analysis.

Data Collection
Malaria incidence data were collected from Ethiopian Public Health Institute for all wards .The Ethiopia Public Health Institute summarized weekly malaria incidence in each ward in the study area between 2015 and 2016 (96 weeks in all). The total number of malaria incidence were 39592.14 over 2015-2016 in the study area. Malaria incidence was computed as malaria incidence divided by population and multiplied by 1000.
The climate and environmental predictors considered in this study, as well as their descriptions, are listed in Table 1. The selected environmental variables are monthly Normalized difference vegetation index (NDVI), elevation, Relative humidity, Temperature and Precipitation. The dataset of elevation, Relative humidity, Temperature and Precipitation is provided by Ethiopian Metrology Agency (EMA). This dataset had station data collected from 132 stations from the country. Whereas, Normalized difference vegetation index (NDVI) along with the spatial reference of the study area was downloaded from the Moderate Resolution Imaging Spectroradiometer (MODIS) instruments on-board the Terra and Aqua satellites (https://ladsweb.nascom.nasa.gov/). For this research work, the MODIS Terra NDVI product (MOD13A3 Version 6), a monthly level-3 composite with a 1 km spatial resolution, was applied to describe the vegetation coverage of each county in each month. Different methods were used in other studies to interpolate environmental data by using deterministic techniques automatically or to estimate the values statistically at the grid x y co-ordinates (Berke, 2004). I applied kriging interpolation to get the value of elevation, Relative humidity, temperature and precipitation for the entire study area. Population data (2012) were collected from the Ethiopian Central Statistical Agency and were used to compute the malaria incidence.

Spatial analysis of malaria
Initially, before applying regression analysis, we generate a malaria risk map, or hot-spots map, using local Gi* statistics (Yeshiwondim et al., 2009): Where, w ij is a geospatial weight matrix at a given distance lag in kilometers (d), (w ij (d)) is 1 for location distance from j to i is within d; otherwise w ij (d) is 0). The existence of hotspot of malaria indicators will be determined based on the value of Z-score. A high positive value of Z > 1.96, showed that the position distinct i is surrounded by relatively high malaria incidence region. In contrast, a high negative Z-score value indicates that the location separates i is surrounded by relatively low (cold spot) malaria incidence in distinct areas. Otherwise, random distribution of malaria incidence for high and negative value of Z ≥-1.96 and ≤ 1.96 (Yeshiwondim et al., 2009).
Anselin's Local Indicators of Spatial Association (LISA) method, particularly the Local Moran's I Statistic (Anselin, 1995), was used to identify and map the local clusters of high malaria incidence rates. LISA calculates a measure of spatial association for each ward locations. A local Moran's I autocorrelation statistic at the location i (Acharya et al., 2018)can be expressed as where z i and z j are the standardized scores of attribute values for unit i and j, and j is among the identi ed neighbors of i according to the weight's matrix w ij .

Regression analysis
Geographically weighted regression (Ge et al., 2017) is a suitable method for spatially varying relationship data analysis. In regression data analysis, for example, ordinary least squares (OLS), generally assume xed relationships between dependent and independent variables in the study area. However, Geographically weighted regression (GWR) lets the regression parameters to differ locally by disseminating location-wise parameter estimates for all independent variables (Fotheringham, Charlton and Brunsdon, 2002). GWR determines the spatial variabiliy of coe cients within the study area, and the explanatory power of explanatory variables is spatially measured for local analysis (Ge et al., 2017). It has been widely used as a tool to explore non-stationarity, and its execution has been improved with new contributions, such as new sets of kernel functions ( The model GWR is appropriate for non-stationary variables (Fotheringham, Charlton and Brunsdon, 2002). In the rst step, the average annual malaria incidence in all two years (2015-2016) was tested for spatial heterogeneity (non-stationarity) with Global Moran's I statistic.
In many studies, to deal with data with zero malaria incidence, the malaria case data were adjusted by a Bayesian model (Ge et al., 2017). The malaria data we used had not consisted of a large number of locations with zero malaria incidence; therefore, we didn't apply the Bayesian model for this study.
In regression, multicollinearity could occur if one explanatory variable was a linear function of another explanatory variable and formerly observed in GWR modeling (Hasyim et al., 2018). The independent variables "altitude," "relative humidity," "precipitation," "NDVI," and "temperature" were tested for multicollinearity. To investigate the colinearity problem among the independent variables, we used indices that are based on the predicted variance of modeling Variance In ation Factor (VIF) (Halimi et al., 2014). We considered the most often applied criteria that establish that variables with VIF greater than 4 warrant further investigations, and those with VIF greater than 10 indicate serious multicollinearity.
Ordinary Least Squares was initially used before the GWR model to examine global statistical relationships between dependent and explanatory variables, including the multicollinearity assumption. At this level, the presence of local variation in relationships was not taken into account in regression. The OLS regression model was used to assess the global relationship between malaria incidence and the selected environmental risk factors. The method of least square expressed in the following equation (Acharya et al., 2018): Where y i is the ith examination of the response variable, a j x ij is the ith examination of the Kth explanatory variable, and ε i is the error terms. The global model assumes that the rate of neighborhood ward i is independent of neighboring j and that residuals usually distributed in terms with zero mean.
Since the study area was characterized by spatial heterogeneity, we used the GWR model as an alternative to examine the local relationship between the dependent and independent variables (Hasyim et al., 2018). With the discussed dependent and independent variables, the GWR model can be formalized as Where y is the value of malaria incidence at the location u, x t is the value of explanatory variable t at the location u, β t (u) is the regression coe cient at the location u, and ԑ is the random error with mean 0 and variance σ².
In the GWR model, each explanatory variable has different regression parameters due to spatially varying parameters in weighted analysis regression (Mar'ah, Djuraidah and Wigena, 2017).
The GWR model that has both local and global parameters is known as Mixed Geographically Weighted Regression or Semi-parametric Geographically Weighted Regression (Nakaya et al., 2005). According to (Mar'ah, Djuraidah and Wigena, 2017), a stepwise procedure that allows all possible mixture of global and local parameters was tested, and the optimum mixed/semi-parametric model was selected based on the smallest corrected Akaike Information Criterion (AICc) value. The spatial variability test (F-Test) was used by the model to determine local parameters in the model (Mei, Wang and Zhang, 2006). The speci ed local and global parameters depend on the con dence interval of GWR coe cients (Mar'ah, Djuraidah and Wigena, 2017).
In the GWR models, a weight matrix is calculated to calibrate the model and distinguish the spatial association among nearby wards. A xed Gaussian kernel function was applied for the weighting scheme (Hasyim et al., 2018). The optimal distance threshold was determined by minimizing the AICc of the model.
A Gaussian kernel is appropriate for xed kernels as it can prevent the risk of there being no data within a kernel (Nakaya, 2016). The golden search method was applied to determine the optimal bandwidth size for geographically weighting e ciently. The optimal bandwidth and the related weighting function were attained by selecting the lowest AICc score. The xed Gaussian kernel for geographical weighting used in this study (Nakaya, 2016) is as follows: 4 Where w ij is the weight value of the observation at the location j to estimate the coe cient at location i, d ij is the Euclidean distance between i and j, and b is the size of the xed bandwidth given by the distance metric. The positive [negative] association between response and explanatory variables can be indicated by a positive [negative] regression coe cient β t (u) of the explanatory variable t at the location u. If one explanatory variable X t (i.e. environmental risk factor) has a positive [negative] coe cient at the location u, it means that when X t increases at the location u, it is expected that the malaria incidence (Y) increases [decreases] at the location u, assuming all other factors remain constant. The selected environmental variables (Elevation, precipitation, temperature, NDVI, and relative humidity) correspond to the explanatory variables, and the pre-processed annual average malaria incidence is the response variable in the GWR and s-GWR models of 2015 and 2016. OLS regressions were also tted for comparison purposes. Diagnostic information provided includes the overall R 2 , AICc, and the analysis of spatial autocorrelation of the residuals.
Some results of the GWR and s-GWR models (e.g., local R 2 , local coe cients, and estimated incidence and residuals) were mapped using the  In contrast, in 2016, the annual malaria incidence hot-spot distribution was along the northern part of the county ( Fig. 3.b). These results also highlight the spatial nonstationary of malaria incidence. Ordinary Least Squares model The coe cients of the Ordinary Least Squares models have the same value for all points within the study area (Table 2.) and (Table 3.). Thus, the global regression models could not capture the process for spatial heterogeneity and varying relationships in the data. In the 2015 model (Table 4), none of the regression coe cients is signi cantly different from zero at the 5% signi cance level (p-value > 0.05), though the coe cient of temperature (TM2015) is signi cant at the 10% signi cance level. In the 2016 model (Table 5) all coe cients are signi cant at the 5% level (p-value≤0.05), except NDVI2016.  The GWR models were used to explore the local effects of variables on malaria incidence in all wards in 2015 and 2016. The independent variables were temperature, elevation, relative humidity, precipitation, and predictor variable derived from remote sensing data (NDVI).
The pseudo-t statistics in the GWR model indicate the statistical signi cance of locally varying coe cients for the explanatory variables. Figure 4 depicts the spatial distribution of pseudo-t values for all independent variables for both years in the study area. Pseudo-t values were computed by dividing independent coe cient estimates by their standard errors, with statistical signi cance de ned as a pseudo-t-value greater than or equal to 1.96 (positive relationship) or pseudo-t value smaller than or equal to -  Fig. 4, with a statistically signi cant positive association in red/orange and negative statistically signi cant relationship in green/light green. Figure 4.(a-j) shows local coe cients for independent variables for both years in the GWR models. It effectively reveals how the direction and strength of the relationship between each predictor and response variable vary over space. Table 4, Table 6, and Table 7 summarize the values of the maps of GWR local coe cients inFigure 4.(a-j), and also show global adjustment measures (R 2 , Adjusted R 2 and AICc). Despite the higher Adjusted R 2 in 2016 model, the 2015 model has a better global t considering its lowest value of the AICc. All these results are further discussed below. In 2015, temperature coe cients showed a positive and negative association with malaria case per wards and were signi cant in some wards located to the northwestern, southwestern part of the study areas Fig. 4g. Elevation 2015 estimated coe cients showed a positive and negative relationship with malaria incidence per ward and was signi cant in some wards located to the northern, southwestern, and southern part of the study areas (Fig. 4i). In 2015, the estimated NDVI coe cients showed a positive and negative association with malaria incidence per wards and were signi cant in some wards located to the northwestern, northeastern and southern part of the country Fig. 4a. In 2015 precipitation estimated coe cients showed a positive and negative association with malaria incidence per wards and were signi cant in some wards located to the western, northwestern, southwestern, and south-central parts of the study area (Fig. 4c). In 2015 relative humidity estimated coe cients showed a positive and negative association with malaria incidence per wards and were signi cant in some wards located to the northern and western part of wards in the study area (Fig. 4e). In 2016 NDVI estimated coe cients showed only positive association with malaria incidence per wards and were signi cant in some wards located to the northeastern wards of the country (Fig. 4b).
In 2016 Precipitation estimated coe cients showed an only negative relationship with malaria incidence per wards and were signi cant in some wards located to the northern part of the country (Fig. 4d). In 2016 relative humidity, temperature, and elevation estimated coe cients showed a positive and negative association with malaria incidence per wards and were signi cant in some wards located to the northern part of the country (Fig. 4h, f, and j). Table 4 Depicts the comparison of the GWR and OLS models based on several indicators. For both years, the sum of the residuals of squares (RSS) was summarized to evaluate the model error, and Global Moran's I of residuals were tested along with the associated signi cance levels. The AICc values showed that the GWR model of each year tted better than the corresponding OLS models. The spatial autocorrelation of residuals was not entirely removed in the 2015 GWR model, but the Global Moran's I statistic was closer to zero in GWR than in the OLS models.
Global Moran's I results showed (Table 4) there is signi cant autocorrelation in the residuals of the GWR model in 2016, and con rms the variables considered in this study were unable to appropriately predict the spatial distribution of malaria incidence in the entire study area. That was due to the scarce population in some wards or missing explanatory variables. In contrast, the Global Moran's I result of spatial autocorrelation of residuals of the 2015 model was not statistically signi cant so that the model was well speci ed.

Semiparametric Geographically Weighted Regression
Semiparametric Geographically Weighted Regression (s-GWR) models were investigated. The GWR model with all local variables (before L -> G selection) was compared with s-GWR models (after L -> G selection), where local variables were step by step selected to become global variables. The best s-GWR models had an AICc of 7273.689 in 2015, and 12304.718 in 2016 (Table 5), thus they performed better than the GWR models ( Table 8). The s-GWR models were further used to explore the local and global relationships of the explanatory variables in connection to malaria case.  In summary, both s-GWR models performed better than the other competing models, thus they are considered the nal models for malaria incidence in this study.
The results of geographic variability test and local to global variable selection approach were based on DIFF of Criterion (Table 7 and Table 8 The s-GWR model with NDVI as global predictor and elevation, temperature, precipitation, and relative humidity as local predictors corresponds to the nal model found in 2015. In 2016, s-GWR model with elevation and temperature as global predictors and NDVI, precipitation and relative humidity as local predictors is the nal model.
The variation of the estimated local coe cients and associated t statistics are shown in (Fig. 5and Fig. 6 below.

Discussion
In this study, the effects environmental variables on malaria incidence were measured by OLS, GWR and s-GWR models for each year, 2015 and 2016, across 679 wards in Ethiopia. In the study area, the high-risk region for malaria, and spatial clustering appeared in the distribution of malaria incidence for both years. All three models considered the same set of explanatory variables, which were temperature, elevation, relative humidity, precipitation, and a predictor variable derived from remote sensing data (NDVI).
The results of this study showed that malaria incidence in Ethiopia during the study period heterogeneously distributed and spatially clustered at the ward level in the country. The results are consistent with research ndings from past studies conducted in various malaria-endemic regions of the world (Delmelle et al., 2016;Wijayanti et al., 2016;Acharya et al., 2018;Lin and Wen, 2011).
This research is the rst ward-level malaria study using the s-GWR model in entire Ethiopia, which explained the modeling malaria incidence associated with environmental risk factors in the country. The nding could be helpful for ward-level planning, policy formulation, and implementation of malaria control.
Our study showed the importance of the semiparametric geographical modeling approach of local-level risk factors analysis by contrasting global (OLS), local (GWR), and mixed (s-GWR) model. Our analysis exhibited the drawbacks of the OLS method to explain spatial variation of malaria incidence in terms of predictive performance and model accuracy and complexities evaluated to the GWR model. We showed that model goodnessof-t could be improved through the implementation of the s-GWR model. These ndings are concurrent with malaria study in Ghana (Ehlkes et al., 2014), and dengue fever in Jhapa district, Nepal (Acharya et al., 2018). However, when independent variables do not show spatial non-stationarity, the ordinary least squares regression model is generally recommended to avoid the model complexity instead of GWR or s-GWR (Ramezankhani et al., 2017).
As a rule of thumb, a "serious" difference between GWR and OLS models generally regarded as one where the dissimilarity in AICc values between the models is at least 3 (Fotheringham, Charlton and Brunsdon, 1998  A signi cant bene t of the s-GWR model is the ability to visually represent the varying strength of association between the response and explanatory variables (Buck, 2016). Moreover, it facilitates the interpretation based on spatial context and known characteristics of the study area (Goodchild and Janelle, 2004). The variation in local R 2 over the wards revealed signi cant regional differences in the malaria incidence transmission process in the study area (Fig. 7a-b).The local R 2 depicted that the local model had higher performance in hotspots areas when it compared to the other parts of the study area matching with previous parallel studies from Nepal  Our nal mixed s-GWR models show that the distribution of annual malaria incidence is heterogeneous (Fig. 5 and Fig. 6)  were signi cantly correlation with malaria incidence that vary strongly at the village level. Identifying the malaria incidence clusters (areas with a high number of malaria incidences) is critical in developing or improving malaria planning and control strategies at the ward scale in the country. Dissimilarities of malaria pattern exist between different regions (Guthmann et al., 2002). Thus in our study also indicated that the pattern of malaria incidence distribution is not the same in the study area; it changes from year to year in the country. The malaria incidence clusters may point to the wards that require prompt notice in terms of planning and implementation of the disease control strategies.  (Nakaya et al., 2005). In our study, the analysis result showed that assuming that some variables vary at the local level, while others have a global effect, substantially improves the model performance. Permitting spatial heterogeneity within the regression model allows clear interpretation regarding the true nature of the potential relationship (Ehlkes et al., 2014). That could be due to the Long-lasting insecticidal nets (LLINs) distributed to some of the wards that have malaria incidence in the country. Longlasting insecticidal nets (LLINs) are a tool to control malaria vector in malaria epidemic areas effectively (Masaninga et al., 2018). When assessing the relationship between environmental variables and malaria incidence, one should think about the pathways in which these variables under study lie (Ehlkes et al., 2014). For instance, the environmental variables: temperature, NDVI, elevation, relative humidity, and precipitation, which in uence the malaria inciencde considered in this study as they determine the plenty of mosquito or their breeding habitats.
In Ethiopia, malaria control strategies include indoor residual spraying (IRS) and LLINs are applied based on the local setting (Loha et al., 2019). Those factors tend to reduce the incidence of malaria. The interaction between these factors and malaria incidence may bring out unexpected results, defying the norms regarding the association between environmental risk factors and malaria disease.
In this research, there was an association between elevation and malaria incidence. Internationally, Anopheline species diversity and density decrease from the lowlands to highlands (Hasyim et al., 2018). Therefore, poor inhabitants living in forested lowland areas in Papua, Indonesia, were found to be at a higher risk of malaria disease than those in the highlands (Hanandita and Tampubolon, 2016).
In contrast, a positive association between elevation and plenty of Anopheles mosquitoes has noticed in the highlands of Ethiopia, Colombia, and Ecuador, mainly in warmer years (Siraj et al., 2014;Pinault and Hunter, 2011;Alimi et al., 2015). It has been accepted that malaria transmission possible decreases as the altitude increases (Chikodzi, 2013;Meyrowitsch et al., 2011). In our study, also we noted elevation was signi cant in 2015 and showed its expected negative relationship with malaria incidence in some of the wards in the northern and southern wards, but also showed a positive correlation in some wards to the western part of the country (Fig. 5a).
In Ethiopia, precipitation was signi cantly correlated with malaria incidence in tropical areas (Midekisa et al., 2015). Moreover, in Botswana, precipitation showed association with the incidence of clinical malaria incidence (Chirebvu et al., 2016). Variations in monthly rainfall in rural Tanzania primarily correlated with malaria incidence (Thomson et al., 2017). In South Africa, the number of malaria incidence was signi cantly positively associated with higher winter precipitation (Kleinschmidt et al., 2001). In this study, coe cients of precipitation in 2015 showed the expected positive and negative relationship with malaria incidence in some wards in the country. Precipitation was signi cant in some rural wards located in the northwestern, western, central, and southwestern part of the country as depicted in Fig. 5b. In Ethiopia, minimum temperatures signi cantly correlated with malaria incidence in cold areas (Midekisa et al., 2015). In this study also local coe cients of temperature in 2015 showed positive and negative relationship with malaria incidence and were signi cant in some wards located in the northwestern and western part of the country, as depicted in Fig. 5c.
Precipitation creates oviposition sites for female mosquitoes, whereas relative humidity is a crucial parameter for adult mosquito daily survival (Day, 2016). Anopheline mosquitoes need stagnant water to wind up their larval and pupal development. Thus, precipitation and relative humidity affect the transmission of malaria by providing water to create aquatic habitats. In this study also local coe cients of relative humidity in 2015 showed the expected positive and negative relationship with malaria incidence, and they were signi cant in some wards located in the northwestern and western part of the country, as depicted in Fig. 5d. Anopheles (Cellia) leucosphyrus is the type of malaria that can be transmitted in forested areas of Sumatra (Elyazar et al., 2013). In 2016, NDVI local coe cients showed an only positive relationship with malaria incidence in some wards in the country. NDVI was signi cant in some wards located in the northern part of the country, as it showed in Fig. 6a. In 2016 precipitation local coe cients showed an only negative relationship with malaria incidence and were signi cant in some wards located in the northern part of the country, as it showed in Fig. 6b. In 2016 relative humidity local coe cients showed a positive and negative relationship with malaria incidence in some wards in the country.
Relative humidity was signi cant in some wards located in the northern part of the country (Fig. 6c). This indicated that s-GWR successfully captured the spatial stationary and non-stationary to model the factors that in uence the spread of malaria incidence.
The weak positive and weak negative relationships between environmental risk factors and malaria occurrences in some of the wards could be due to the protective effect of malaria control factors, for example, vector control methods including LLINs and IRS. These malaria interferences contribute signi cantly to the decline in malaria incidence, mainly in areas progressing towards malaria elimination (Meyrowitsch et al., 2011). Researchers (Gwitira et al., 2015) also noted that in malaria incidence where there is effective malaria control, there would be weak correlations among habitat suitability and malaria incidence. This was observed in this study in 2015, NDVI was a weak association with malaria incidence in the country. In 2016 elevation and temperature were also weak correlations with malaria incidence in the country. Temperature, precipitation, and relative humidity are frequently used to predict for the spatial, seasonal, and interannual variation for malaria transmission, such as the dynamic malaria model forecasting malaria occurrence with seasonal climate (Hoshen and Morse, 2004). Land use, relative humidity, elevation, and precipitation have been identi ed by GWR to determine the regional vulnerability to malaria incidence in Purworejo, Indonesia (Hasyim et al., 2018). The GWR model revealed here in our study that elevation, temperature, precipitation, relative humidity, and NDVI signi cantly in uence malaria incidence in some wards in Ethiopia. Similarly, in 2015 elevation, temperature, precipitation, and relative humidity have been identi ed by s-GWR and were signi cantly in uence malaria incidence in some of the wards in Ethiopia. Similarly, in 2016 precipitation, NDVI, and relative humidity have been identi ed by the s-GWR model and were signi cantly in uence malaria incidence in some wards in Ethiopia. However, s-GWR model allowing for spatial heterogeneity explains better the relationship of malaria incidence with environmental risk factors in Ethiopia. Similarly, in Venezuela, the GWR model analysis showed that ecological relations that act on different scales play a role in malaria transference and that modeling increases the understanding of important spatiotemporal inconsistency (Hasyim et al., 2018).

Conclusion
This research explored and analyzed the modeling spatial distribution of malaria incidence and its association with environmental risk factors in Ethiopia. The nding of this research showed that malaria incidence distribution in Ethiopia was heterogeneous and highly clustered at the ward level. All environmental variables considered (elevation, temperature, relative humidity, participation, and NDVI) were the most important risk factors responsible for the spatial variation of the disease incidence.
The key task for malaria elimination should be built systems and tools to reduce disease burden where malaria transmission is high locally. By comparing GWR and s-GWR against the global regression model, in both 2015 and 2016, it becomes apparent that GWR and s-GWR models yielded Declarations Availability of data and materials The data sets used and/or analyzed during the current study are available at Ethiopian Public Health Institute and Ethiopian Metrology Agency. new information about malaria incidence that varies over space. In our study, the variability of malaria incidence over space was due to environmental and geographical local differences (Loha and Lindtjørn, 2010). The s-GWR models provided better ts when compared with the results of the local GWR and global OLS models.
The ndings of this research have a direct implication for health policy planning and decision making. Malaria being a highly focal disease, health authorities should always consider selecting district-geographical areas: in this case, the wards rather than zones for control and intervention program. The method adopted could be an essential tool to locate such high-risk areas. Moreover, this research shows the relevance of a mixed geographical regression modeling approach in geostatistics analysis of disease and other phenomena in uenced by complex environmental factors at the ward or local scale. This research inherits some limitations which need to address in the future study. We could not include some essential social-economic variables such as Gross Domestic Product (GDP) and migration patterns in our analysis due to data unavailability. Regardless of these limitations, this is the rst spatially explicit malaria incidence study in Ethiopia to map and explore environmental risk factors in the entire country at the ward-level. The methodological framework implemented in this study is convertible in other regions and at different spatial scales depending upon the data availability, as well as to other climate-related diseases. Moreover, this study demonstrates the importance of a mixed s-GWR modeling approach in the spatial analysis of malaria incidence affected by complex environmental risk factors at the ward-level.
This research also revealed the importance of local geographical modeling (e.g., s-GWR) approach to improve the knowledge about malaria incidence and its determinants, so that this study can be used for the control and management of malaria disease at the ward level.
Future studies should consider including more risk factors that may further improve the performance of the s-GWR models in determining the local variation of malaria incidence.