Seasonal and spatial variations of malaria transmissions in northwest Ethiopia: Evaluating climate and environmental effects using generalized additive model

Abstract

The impacts of climate change and environmental predictors on malaria epidemiology remain unclear and not well investigated in the Sub-Sahara African region. This study was aimed to investigate the nonlinear effects of climate and environmental factors on monthly malaria cases in northwest Ethiopia, considering space-time interaction effects. The monthly malaria cases and populations sizes of the 152 districts were obtained from the Amhara public health institute and the central statistical agency of Ethiopia. The climate and environmental data were retrieved from US National Oceanic and Atmospheric Administration. The data were analyzed using a spatiotemporal generalized additive model. The spatial, temporal, and space-time interaction effects had higher contributions in explaining the spatiotemporal distribution of malaria transmissions. Malaria transmission was seasonal, in which a higher number of cases occurred from September to November. The long-term trend of malaria incidence has decreased between 2012 and 2018 and has turned to an increased pattern since 2019. Areas neighborhood to the Abay gorge and Benshangul-Gumuz, South Sudan, and Sudan border have higher spatial effects. Climate and environmental predictors had significant nonlinear effects, in which their effects are not stationary through the ranges of values of variables, and they had a smaller contributions in explaining the variabilities of malaria incidence compared to seasonal, spatial and temporal effects. Effects of climate and environmental predictors were nonlinear and varied across areas, ecology, and landscape of the study sites, which had little contribution to explaining malaria transmission variabilities with an account of space and time dimensions. Hence, exploring and developing an early warning system that predicts the outbreak of malaria transmission would have an essential role in controlling, preventing, and eliminating malaria in areas with lower and higher transmission levels and ultimately lead to the achievement of malaria GTS milestones.

1. Introduction

In 2020, 241 million malaria cases occurred globally, which is more than 14 million cases compared to 2019, which might be due to service disruption and restriction of the COVID-19 pandemic. The WHO African region is the most affected region and off-track from the Global Technical Strategy (GTS) for malaria 2016–2030 targets of reducing malaria incidence compared to a 2015 baseline. The region accounts the 95% and 96% of global cases and deaths in 2020, respectively. The malaria incidence trend has stalled progress globally since 2018 due to the availability of a limited set of tools and approaches of malaria prevention, controlling, and elimination techniques [1,2]. In 2020, malaria incidence significantly decreased in Ethiopia, reduced by more than 40% of cases in 2015, and the GTS 2020 target was achieved. However, the world malaria report revealed that Ethiopia had disrupted the progress of decreasing malaria case incidence since 2019 [1].

Malaria transmissions are highly heterogeneous in Africa, varied across the urban and rural settings. The rural areas are more exposed to malaria transmission since malaria vector population sizes have higher density and diversity in the rural areas. However, studies suggest that malaria transmission has been increased in most cities since 2003 in Sub-Saharan Africa [3]. East and southern African countries have high malaria transmissions with a high malaria risk, and most of them have a stable malaria transmission; however, Ethiopia has highly seasonal transmissions [[4], [5], [6], [7]]. A study using the malaria surveillance data at Jimma town suggests that malaria case incidence has a seasonal variation in 2000–2009, in which the highest cases occurred from September to November. A study in northwest Ethiopia also revealed that malaria had significant seasonal variations and occurred following the Kiremt seasons from June to September [6,[8], [9], [10]]. Malaria transmission has seasonal variation and had a declining linear trend between 2012 and 2020 in the Amhara region of Ethiopia, with a higher seasonal index in October- November [11].

Climate change influences were severe on the population's health outcomes in the developing countries less responsible for global warming. Infectious diseases could be exacerbated in the future through the heating of the globe [12,13]. Africa experienced the ideal temperature of malaria transmission, and seasonal variation is shifting to the Sub-Saharan coastal areas due to global warming and climate change [14]. However, the effects of climate change on malaria prevalence have been debated and varied across the landscape, land cover change, altitude of study sites, and study periods [5,12,15].

The complex interplay of climatic, environmental, and socio-economic factors are attributed to the dynamics of malaria incidence trends, and temperature and precipitation are highlighted as the essential drivers of malaria epidemics [6,16,17]. Moreover, study findings suggest that temperature magnitude and seasonality are fundamental climate variables that constrain malaria transmission [12,15]. Air temperatures below approximately 18 °C and 15 °C, respectively, prohibit the development of the Plasmodium falciparum and Plasmodium vivax parasites responsible for most malaria cases in Ethiopia [15]. Areas in the highlands have a temperature below the malaria transmission thresholds; however, the threshold elevation changes with time and found a significant increase in elevation of temperature thresholds, and malaria is found to have substantial inter-annual and spatial variations at the highlands of Ethiopia [15].

A study conducted in Jimma town showed that malaria was significantly associated with minimum temperature, total rainfall, and maximum temperature at one month lagged effect [7]. Malaria incidence has been associated with monthly minimum and maximum temperature in most regions of Ethiopia [5]. However, the maximum temperature had no significant effects on the malaria transmission in accounting spatial, temporal, and space-time effects of districts in the Amhara region. On the contrary, minimum temperature and total rainfall were found to have a positive significant linear effect on the log-scale of the number of malaria cases in northwest Ethiopia [8]. Generally, study findings suggest that length of rainy season, maximum temperature, minimum temperature, relative humidity, variation of altitude, land surface temperature, normalized difference vegetation index, enhanced vegetation index, actual evaporation, total rainfall, soil moisture were climate variables found to have a significant effect on malaria transmission; however, its effects varied across areas and unit of analysis such as individual, village, district, zone, region, or country level and statistical model that used to analyze the data [5,6,8,[18], [19], [20], [21], [22]].

Transmission of malaria is heterogeneous across areas and varied through time in Ethiopia. Further, malaria transmission has spatial, temporal, and spatiotemporal variation in both stable and unstable transmission areas in Ethiopia's northern and northwestern districts. The Amhara region also had significant spatial, spatiotemporal clusters with an elevated malaria risk that occurred in a varied length of time [10,11,21,23,24]. Further, the prevalence of malaria transmission intensity was heterogeneous and changed with the average area elevation. The spatial-temporal variation of malaria is also attributed to the suitability of weather conditions for the abundance of Plasmodium parasite vectors [14,25].

Climate change has increased infectious diseases occurrences, and the relationship pattern depends on the form of climate change and details of host-pathogen systems [26]. However, with the account of spatial, seasonal, and inter-annual variations, evidence suggests that climate, along with many factors, can affect infectious diseases in a nonlinear fashion [27]. The generalized additive models are used to identify the more precise nonlinear effects of climate variables on malaria incidence considering spatial, temporal, and spatiotemporal random effects and variations [22,28]. Few studies were conducted in the study areas at different periods, and the number of districts included was not comprehensive in the inclusion of areas with lower and higher malaria transmission levels [6,8,10,15,21,29]. However, there have not been enough studies thus far that estimate seasonal effects, trends, spatial, space-time interaction effects, and nonlinear effects of climate and environmental factors on monthly malaria cases incidence of districts in the Amhara region of Ethiopia, under lower and higher transmission settings, in accounting temporal and spatial autocorrelations. This study is aimed to investigate variations of seasonal and long-term trends of malaria cases across districts of the study region with the inclusion of nonparametric effects of environmental covariates.

2. Materials and methods

2.1. Study area

This study was conducted in northwest Ethiopia, included more than 20 million population and located from 9°20′ to 14°20′ north latitude and 36° 20′ to 40° 20′ east longitude. The study area encompasses different ecological zones with an elevation range from 506 to 4533 m [30]. In this study, we included 152 districts where the third level administrative units in Ethiopia, where the initial malaria elimination program has been planned, and weekly malaria surveillance data were reported to Ethiopian and regional Public Health Institute.

2.2. Study design and period

Retrospective studies investigate a phenomenon, situation, problem, or issue in the past. They are usually conducted based on the data available for that period or on respondents' recall of the situation [31]. A retrospective study methodology was used to explore the nonparametric effects of environmental variables on malaria incidence. This study was based on monthly malaria cases of districts in northwest Ethiopia between July 2012 and June 2020.

2.3. Data

To address this study's objective, we have employed several datasets such as monthly malaria surveillance, environmental variables, district population sizes, and district spatial data. The weekly malaria surveillance data of districts in the Amhara region were obtained from the Amhara Public Health Institute. The weekly count data were reported using the WHO epidemiology week (EPI-week) from Sunday to Saturday. The data includes weekly malaria incidence reports of all confirmed cases, either by microscopy or rapid diagnostic test, and clinical cases identified by skilled professionals. The data covered the eight fiscal years of Ethiopia, which is between July 2012 and June 2020. Ethiopia's fiscal year started on 8th July, and the Amhara Public Health Institute (APHI) diseases surveillance reporting week is started on EPI week 28, falling on the first week of July. The monthly malaria counts are calculated by adding the corresponding weekly malaria cases considering an EPI-week had at least four days in a given month. The levels of hospitals were varied in the study area, and some districts have higher-level hospitals such as referral and specialized hospitals where patients may come across districts for treatment either by referral letters or not. Considering malaria cases from higher-level hospitals would influence the monthly incidence of malaria in districts where higher level hospital located and would have an overestimate smoothed effects of environmental factors. Hence, we excluded malaria cases of referral and specialized hospitals in determining monthly malaria cases of districts.

The monthly data of environmental predictors were obtained from satellite data which was retrieved from the US National Oceanic and Atmospheric Administration (NOAA), Giovanni open data portal of NASA, Climate Hazard Center InfraRed Precipitation with Station data (CHRIPS) [32], and database of global climate and weather data (WorldClim.com). District-specific values for climate variables were estimated using interpolation methods from the satellite, and the model reanalyzed climate data at a spatial resolution of 100 × 100 m using ArcMap 10.3 [33].

The number of malaria cases was varied among districts, and the spatiotemporal distribution of malaria incidence was comparable if they were adjusted to the population size in a given interval of time [34]. Due to the transmission of maternal antibodies, infants are supposed to be protected against malaria throughout their first months of life. However, in a higher transmission settings, malaria in early infancy is not rare, and vulnerability to the infections might be varied among individuals, and the prevalence of disease was higher than previously preserved thoughts [35]. Meanwhile, adjusting the number of malaria cases using yearly estimated population size might lead to biased predictions of the spatiotemporal distribution of malaria burden in the region. Hence, monthly estimated population size of districts was used as an offset variable in the Bayesian generalized Poisson model. The monthly estimated population sizes of districts in 2014–2017 and 2018–2020 were obtained from the central statistical agency of Ethiopia [36] and Amhara National Regional State Plan Commission, respectively. The estimated monthly population size of districts between 2012 and 2013 was estimated based on the estimated population growth rate of districts in 2012 and 2013, and the 2007 population and housing census count of districts in the region.

The study area shapefile was obtained was obtained from the Map Agency of Ethiopia and Central Statistical Agency (CSA) of Ethiopia, and spatial centroid coordinates (latitude and longitude) of districts were created in ArcGIS 10.3 and R version 4.0 to evaluate the smoothed effects of environmental factors on the monthly malaria cases at the district level.

2.4. Statistical analysis

The effect of climate variables on malaria case incidence were assessed with consideration of season, spatial, and spatio-temporal variations using spatio-temporal generalized additive model. Let $Y_{it}$ denote the monthly malaria cases and $E_{it}$ the expected counts in district $i$ and month $t,i=1,\dots ,I;t=1,\dots ,T=12$. The expected count $E_{it}$ is calculated using internal standardization in considering the population sizes of districts. The monthly malaria case is a count variable and would be modeled using count regression models. Under the assumptions of independence and equi-dispersion, the Poisson regression model is commonly used to examine rates of areal units. However, modeling count data presents numerous issues, particularly when the data contains a large number of zeros and is over-dispersed [37]. Further, independence and equi-dispersion assumptions might not be appropriate due to dependence in individual response, contagion, clustering, heterogeneity, and exclusion of some casual factors of the disease [38,39]. The over-dispersion problems in modeling count data can be solved by fitting negatively binomial, quasi-Poisson, and generalized Poisson regression models. The relationship of malaria transmission with climate and environmental factor is debatable, and the effects of the environmental covariates are not homogeneous across their ranges and nonlinear [28]. Hence, we use generalized additive models (GAM) to explore the relationship between monthly malaria cases and environmental factors with count regression models such as Poisson, negative binomial, and zero-inflated Poisson distribution with a logarithmic link function. The data were fitted using Poisson, negative binomial, and zero-inflated Poisson (ZIP) spatiotemporal generalized additive model, and the best model is selected using Akaike information criterion (AIC) [40]. The general space-time GAM model of the expected number of malaria cases in district $i$ and time $t$ is given as follows:

$$\mathrm{g}\left({\mu }_{it}\right)=\alpha +Z_{it}^T\beta +\sum f_j\left(X_j\right)$$ (1)

A spatial-temporal GAM for modeling monthly malaria cases is obtained by expanding the model given in equation (1) above and formulated as follows:

$$\mathrm{g}\left({\mu }_{it}\right)=\alpha +\log \left(E_{it}\right)+\sum f_j\left(X_j\right)+f\left(Month\right)+f\left(Year\right)+f_{MY}\left(Month,Year\right)+f_S\left({\mathit{x}}_i\right)+f_{ST}\left({\mathit{x}}_i,Month\right)+f_{ST}\left({\mathit{x}}_i,Year\right)$$ (2)

The $\mathrm{g}\left({\mu }_{it}\right)$ is a log link function of the expectation of the response; α denotes the intercept and $\log \left(E_{it}\right)$ is the size population at risk for district $i$ and time $t$ included as an offset to adjust monthly malaria data by population. The $f_j\left(X_j\right)$ is a smooth function of environmental covariates and are modeled as thin plate regression spline functions [41]. The $f_j\left(X_j\right),j=\mathrm{1,2},\dots ,pandf\left(Year\right)$ are modeled using thin plate regression splines and takes the form:

$$f_c\left(w\right)=\sum _i{\delta }_i\left(\left|\mathit{w}-{\mathit{w}}_i\right|\right)+b_1+b_{2}w$$ (3)

Where ${\delta }_i\text{,}$ $b_{1}and{b}_2$ are coefficients to be estimated and $\mathit{w}$ environmental covariates and year.

The choice of knots and number of basis functions may have a substantial impact on modeling results and which is avoided by using a large number of basis functions and at the same time imposing a penalty to ensure that the fitted model is smooth; hence model flexibility is controlled by a smoothing parameter rather than the basis dimension [[41], [42], [43], [44]]. The roughness penalty associated with the tensor product regression spline basis is incorporated in fitting a smoothing effects of covariates in the model and defined as:

$$J_c\left(w\right)={\int \left[\frac{d{f}_c\left(w\right)}{dw}\right]}^{2}dw={\mathit{\alpha }}^{\mathit{T}}{\mathit{S}}_{\mathit{w}}\mathit{\alpha }$$

where ${\mathit{S}}_{\mathit{w}}$ contains known coefficients, and α are the parameters.

The $f_T\left(Month\right)$ given in equation (2) is a cyclic cubic regression spline for months of a year to control seasonality in the data [45]. The smooth function of month of year would not change discontinuously at the year-end, and the default spline will match at the smallest and largest x values. The cyclic cubic regression spline is defined as [45]:

$$f_T\left(Month\right)=\sum _{i=1}^{k-1}{b}_i\left(x\right){\beta }_i$$ (4)

with a second order derivative penalty $\underset{x_1}{\overset{x_k}{\int }}{\left[f^{″}\left(x\right)\right]}^{2}dx={\mathit{\beta }}^T\mathit{S}\mathit{\beta }$ term.

The spatial dependence of the data is incorporated using a smooth interaction function between the latitude and longitude coordinates of each district centroid and denoted $f_S\left({\mathit{x}}_i\right)=f_S\left(Lat,Long\right)\text{,}$ which is given in equation (2) [46]. The two-dimensional thin plate regression spline (TPRS) applied to the geographical locations for the centroids of the neighborhoods districts. A major feature of a two-dimensional TPRS is the isotropy of the wiggliness penalty; smoothing in all directions is treated equally, often considered to be desirable for modeling the interaction between two variables on the same scale, such as geographic coordinates [45]. Other spatial smoothing techniques, such as Markov random field (MRF), often fitted using Markov chain Monte Carlo (MCMC) techniques could be considered, but it exhibits slow mixing [47]. A thin plate regression spline is applied in this study primarily for its computational efficiency with large datasets [48]. Let $f_S\left(u,v\right)$ denotes $f_S\left(Lat,Long\right)$ and the two-dimensional TPRS of $\mathit{s}={\left(u,v\right)}^T$ can be defined as:

$$f_S\left(u,v\right)=\sum _i{\delta }_i\theta \left(\left|\left|\mathit{s}-{\mathit{s}}_i\right|\right|\right)+b_1+b_{2}u+b_{3}v$$ (5)

where ${\delta }_i,i=\mathrm{1,2},\dots ,n,b_1,b_2,b_3$ are coefficient to be estimated, ||. || denotes the Euclideannorm, $\theta \left(r\right)=\frac{1}{16\pi }{r}^2\log \left(r^2\right)$ for $r>0$ and 0 for $r=0$ which is subject to identifiability constraint and wiggliness of the smooth function is penalized using a penalty function.

The ${\mathrm{f}}_{\mathrm{M}\mathrm{Y}}\left(\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h},\mathrm{Y}\mathrm{e}\mathrm{a}\mathrm{r}\right)$ given in equation (2), is a smooth function month-year interaction to evaluate seasonal variation across years between 2012 and 2020. The ${\mathrm{f}}_{\mathrm{M}\mathrm{Y}}\left(\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h},\mathrm{Y}\mathrm{e}\mathrm{a}\mathrm{r}\right)$ is modeled as a tensor product smoother [46]. The tensor product smoother is formulated by first representing smooth functions for each bivariate variable. Tensor product smoother often performs better than isotropic smoother when the covariates of a smooth are not on the same scale. This study used cyclic cubic regression spline and thin plate regression spline basis functions for month and year, respectively [45].

The space-time interactions are incorporated using two tensor product smooth functions such as $f_{ST}\left({\mathit{x}}_i,Month\right)$ is a tensor product smooth function for the interaction of spatial and seasonal effects, and $f_{ST}\left({\mathit{x}}_i,Year\right)$ is a tensor product smooth function of annually varying coefficients of the marginal spatial smooth. The space-time interaction is constructed as a three-dimensional tensor product smooth of space and time [49], which involves firstly specifying the marginal smooth for the time period $f_t\left(t\right)$ in month, and year and a two-dimensional marginal smooth for space $f_S\left(u,v\right)$. The interaction between space and time, which is given in equation (2), is constructed by allowing the temporal smooth $f_t\left(t\right)$ to varying smoothly within the space dimensions u and v and the tensor product smooth function is given as [45]:

$$f_{st}\left(u,v,t\right)=\sum _{r=1}^R\sum _{m=1}^M{\beta }_{rm}{b}_m\left(u,v\right)a_r\left(t\right)$$ (6)

Where ${\beta }_{rm}\text{,}$ in equation (6), are the coefficients of basis functions of tensor product smooths, and the penalty of the space-time interaction term is composed of two components i.e., a penalty of spatial and temporal smooth to the temporally varying coefficients of the marginal spatial smooth with respect to the time scale considered in the tensor product smooth such as month (seasonality) and year (long-term trend).

2.4.1. Model fitting

The generalized additive models with correlated data are fitted using penalized likelihood approach that avoids the mixed model approach's complexity and the Bayesian approach's high computation cost. The maximization of penalized likelihood approach by Fisher scoring is equivalent to the penalized iteratively reweighted least squares (PIRLS) scheme [50]. To estimate the coefficients ($\mathit{\beta })$ of the basis functions of the covariates, a penalized likelihood is used. Let D be a specified penalty matrix and $\mathit{\lambda }>0$ be a smoothing parameter. The $\mathit{\beta }$ is estimated by maximizing the log-likelihood function [51] and given as:

$$\sum _{i=1}^{n}l\left(y_i,{\mu }_i\right)-\mathit{\lambda }{\mathit{\beta }}^{\mathit{T}}\mathit{D}\mathit{\beta }$$ (7)

The smoothing parameters (λ) included in equation (7) controls the trade-off between fit and smoothness, can be selected using minimizing of the generalized cross validation (GCV) score, if the scale parameter has to be estimated, the generalized Akaike's information criterion (AIC), marginal likelihood (ML), and restricted maximum likelihood methods [45,50]. Reiss &Todd Ogden [52]showed that a restricted marginal likelihood (REML) approach offers practical reliability merits, in being less prone to multiple local optima and consequent under smoothing. Further, studies based on simulation also suggest that REML and ML methods improve the mean square error performance relative to the generalized cross validation (GCV) and AIC in most cases. A REML estimation tends to be better than ML in terms of bias and confidence interval coverage of smooth functions when the spatial sample size is small [53]. We used REML to estimate and select smoothing parameters [54].

2.4.2. Model selection

The model was fitted using Poisson, negative binomial, and zero-inflated Poisson distributions and considered main effects and inclusions of space and time interaction effects. Under each model, model selection was carried out using an argument select = TRUE in the bam function of mgcv R-package, which penalizes functions in the null space of the penalty matrices for each model [55]. The choice of link function of the model was performed by comparing their Akaike information criterion (AIC) [56], deviance, percentage of deviance explained [57].

2.4.3. Residual diagnosis

The model diagnoses are checked using residual plots; however, residual plots from count regression generally impose great challenges for visual inspection and are less informative due to the discreteness of the data [58]. The randomized quantile residual has tremendous statistical power for detecting many model misspecifications for count regression models and plotted using gam. check R function, especially for negative binomial and Tweedie distributions [58,59].

2.4.4. Ethical clearance

This research protocol was approved by the College of Science Ethical Review Board, Bahir Dar University, with a letter referenced as PGRCSVD/137/201. The ethical review board waived participant consent since the study was conducted using district-level monthly aggregated malaria data.

3. Results

3.1. Model comparison results

The spatiotemporal GAM was fitted using negative binomial, Poisson, zero-inflated Poisson, zero-inflated negative, and generalized Poisson distributions. We found that negative binomial (NB) is relatively the best fit with AIC, percentage of deviance explained, and R-square (adjusted) are 142327.7, 93.9, and 0.863, respectively. The smoothed effects of environmental covariates and space-time distribution of monthly malaria incidence were investigated using spatiotemporal GAM using a negative binomial distribution.

The variable selections and relative contributions of space, seasonal, and long-term trend for modeling the space-time malaria case incidence was performed by excluding space, time, and space-time interaction from the full model. The model selection was carried out by setting select = TRUE in the bam function of mgcv package in R. The variable selection result indicates that spatial was the strongest predictors and the trend had the second strongest explaining effect for malaria incidence of districts in the study region since excluding these variables results in the most substantial changes in the measure of explained deviance (Table 1). The model with space, seasonal, trend, and space-time interaction terms improved the model fit and has a superior performance (AIC = 142327.7, R-square (adj.) = 0.863, explained deviance = 93.9%) over the additive effects of space, seasonal, and trend components. However, excluding environmental and climate variability had little diminish in the explained deviance and R-square (Table 1).

Table 1.

Evaluation of the contribution of space, seasonal, and trend effects for modeling malaria incidence by excluding predictors from the full model, using AIC and percentage of deviance explained, northwest Ethiopia, 2012–2020.

Model	AIC	Deviance	Percentage of deviance explained
Full	142327.7	15756.84	93.9
-without space × time (seasonality)	145193.8	15693.83	91.9
-without space × time (Trend)	150692.1	15698.82	87.4
-without seasonality × trend	153416.5	13838.3	84.1
-without spatial effect	167499.1	17016.69	59.8
-without seasonality	148344.6	15765.44	89.7
-without trend	157997.2	15945.72	78.9
-without climate and environmental effects	144971.6	16075.14	92.6
-without space-time effects (Traditional-GAM)	203109.7	70406	49.4

The model adequacy checking was performed using gam. check function from the mgcv R package. S1 Fig. 1 presents a Q-Q plot of deviance residual, residual versus linear predictor, response vs fitted values, and histogram of residuals of the selected full model. The Q-Q plots of the residual of the full model revealed that the count regression model with medium and larger values of the residual falling outside of the simulated envelopes might be attributed to the count nature of the response variables and no severe indication of the inadequacy of the model. The relationship between linear predictors and residuals had no noticeable linear pattern and revealed that the model had no inadequacy in excluding potential predictor variables.

Fig. 1.

Smoothed effects of covariates (a) seasonality, (b) long-term trend, (c) altitude, (d) soil moisture, (e) land surface temperature, and (f) Rainfall. The x-axis represents observed data points. The y-axis denotes effect size of variables. Dashed lines indicate 95% confidence intervals, northwest Ethiopia, 2012–2020.

3.2. Spatial and temporal variations, and effects of climate variability

The full space-time GAM (ST_GAM) included the main effects and interaction effects of seasonality, trend and space. The deviance explained, and the R-squared of the full ST-GAM was higher than the sub-models. The 86.3% of the variation of the dependent variable was predictable using the model, and the percentage of deviance explained was 93.9%. Model fitting and variable selection are presented in Table 2 and indicated that environmental factors had significant smoothed (non-linear) relationship since their P-values were less than 0.05, but the relative humidity had a higher p-value compared to the 5% level of significance. The effective degree of freedom (edf), summary statistic of GAM, showed that monthly malaria cases had a higher non-linear relationship with climate variable since their edf were greater than two. However, testing the smooth terms of the relative humidity (edf = 0.53, p-value = 0.123 > 0.05) revealed that its effects was reduced to a linear relationship, and it had a decreasing linear effect on the log-link scale of monthly malaria cases of the districts in the study region. The spatial variation of malaria transmission were represented using 129 smooth terms, and they were found to be significantly different from zero. Besides this, seasonality and trend of malaria cases were represented using nearly 9 and 6 smooth terms and a significantly different smooth terms were estimated. As a result, malaria transmission had significant long-term trend, seasonality and spatial variations in the districts of the study region. Furthermore, the space-time interaction result revealed that malaria's long-term trend and seasonality varied across spaces. Further, the seasonality of malaria cases had also a significant smoothed variations through the study years (Table 2).

Table 2.

Effects of parametric covariates and approximate smoothed effects of environmental, spatial, temporal, and space-time dimensions, northwest Ethiopia, 2012–2020.

Factors	Estimate	Std.Error	t-value	p-value
Intercept	−7.59	0.325	−23.38	<0.01
Smooth terms	edf		F	p-value
s(Month)	8.83		23.7	<0.001
s(Year)	5.88		114.91	<0.001
s(Longitude, Latitude)	129.84		296.26	<0.001
s(Elevation)	17.32		98.27	<0.001
s(Soil moisture)	5.18		1.55	<0.001
s(Land surface temperature)	6.26		2.66	<0.001
s(Rain fall)	4.33		1.17	<0.001
s(Minimum temperature)	3.60		0.94	<0.001
s(Maximum temperature)	4.13		0.59	<0.001
s(NDVI)	14.92		6.63	<0.001
s(Relative humidity)	0.53		0.04	0.123
ti(Year, Month)	62.09		40.17	<0.001
ti(Year, Longitude,Latitude)	607.73		12.79	<0.001
ti(Month, Longitude,Latitude)	413.07		2.53	<0.001
theta = 6.441, R-Square(adj.) = 0.863, Percentage of deviance explained = 93.9%, Deviance = 15756.84

*NDVI: Normalized difference vegetation index; edf: effective degrees of freedom, s: smoothed effect, ti: tensor product effect remaining after removing the main effects.

The smoothed effects of seasonality, trend, and environmental factors on the monthly malaria cases were estimated and displayed in Fig. 1. Malaria transmission has a significant seasonal variation and is given in Fig. 1a. The plot indicates that malaria transmission increased sharply between February and November and peaked around September–November. The highest cases have occurred following the main rainy seasons between June and August. The long-term trend of malaria incidence is depicted in Fig. 1b. The malaria transmission trend decreased sharply between 2012 and 2014, followed a similar trend between 2014 and 2016, followed by a sharply declining trend from 2016 to 2018, and then increased after 2018. Malaria transmission trend is not easily represented using either decreasing or increasing line, and it had wiggliness patterns of transmission through years between 2012 and 2020. Meanwhile, the malaria burden were reached at the bottom level in 2018 in the study region.

The nonparametric spline terms for some climate and environmental variables of the full model are estimated and presented in Fig. 1c–f. Monthly malaria cases incidence was significantly varied with the average altitude (elevation) of districts in considering seasonal, trend, and space-time effects. The effects of average altitude of districts were varied across its ranges, and areas whose average altitude between 1000 and 2000 m are favorable for a higher malaria incidence. However, the point estimate revealed that districts whose average altitude is greater than 2000 m have a lower malaria incidence (Fig. 1c). In addition, districts whose average altitudes were lower than 1000 m and greater than 3000 m had smaller estimated effects, which indicates that they had a lower risk of malaria transmission. The favorable ranges of soil moisture, land-surface temperature, and rainfall for malaria transmission are depicted in Fig. 1d–f, indicating that the point estimate of the smoothed effects was varied through the ranges of values to the corresponding climate and environmental factors. The estimated coefficients of the spline terms revealed that soil moisture had no parametric effect, and malaria transmission is favorable with a percentage of soil moisture in 15–33 (Fig. 1d). The land-surface temperature at 0–10 cm depth had a nonlinear effect, and a land surface temperature approximately within a range of 15–25 °C would be favorable for malaria transmission levels in the region (Fig. 1e). The result also revealed that the highest estimated effect of land surface temperature occurred nearly between 20 and 22 °C, which would be the most favorable range for a higher malaria transmission in the study region. Districts with higher rainfall would be prone to malaria transmissions, and the smoothed line revealed that monthly total rainfall above 250 mm would have a positive effect on malaria risk (Fig. 1f). However, the 95% credible interval revealed a horizontal line that passed within the confidence interval bands at zero for environmental and climate factors (Fig. 1c–f).

The estimated spline terms of minimum and maximum temperature, normalized difference vegetation index, relative humidity and spatial variations are presented in Fig. 2, indicating that its effects varied in ranges of values of the variables. Fig. 2a and b presents the smoothed effects of minimum and maximum temperature and revealed that a horizontal line pass through 95% confidence band; however, estimated basis coefficients decreased with an increase of temperature. We found that the relationship between malaria incidence and NDVI differed across the NDVI values, and areas with a NDVI less than 0.2 or greater than 0.8 had decreased impact on malaria incidence (Fig. 2c), while relative humidity had a linear and a negative relationship with malaria incidence (Fig. 2d).

Fig. 2.

Smoothed effects of covariates and tensor products (a) minimum temperature, (b) maximum temperature, (c) NDVI, (d) relative humidity, (e) spatial effect, and (f) two-dimensional tensor products of months and years. The x-axis represents observed data points. The y-axis denotes effect size of variables. Dashed lines indicate 95% confidence intervals, northwest Ethiopia, 2012–2020.

The bottom-left panel of Fig. 2 displays the two-dimensional tensor product smoother of northing and easting of districts, which clearly shows spatial variability of malaria transmission. The result revealed that localized differences in the underlying attributes of neighborhoods could have a statistically significant impact on malaria incidence. The malaria incidence was higher in the western, northwestern, and northern parts of the region. More specifically, areas in the Abay gorge, areas neighbors to the Benishangul-Gumuz region, and the Sudan border had higher malaria transmissions (Fig. 2e).

The two-dimensional tensor product smoother of month and year, excluding the main effects, is displayed in Fig. 2f and reveals the presence of a nonlinear significant interaction effect. Once we have adjusted seasonal and long-term trend effects, the remaining season-trend interaction effect indicates that the more prominent effects were varied through months and years, which occurred from July to December in 2016–2019. On the contrary, there were much lower malaria incidents throughout the study years, from January to June.

The spatial-temporal interaction term reveals that seasonality and long-term trends have changed after accounting for the main effects (Fig. 3). Areas with similar malaria transmission were represented by contour lines, and the coefficients of the smooth terms were depicted using blue to yellow colors representing low to higher smoothing coefficients. The three-dimensional smoothed effects of space and year are displayed in Fig. 3a, indicating that spatial variation has a statistically significant impact on malaria incidence. The spatial effects were higher in 2012–2014 and occurred in the western parts of the region. The spatial effects were decreased between 2015 and 2018 and increased in 2019 and thereafter (Fig. 3a). The maps of coefficients of the smooth terms in 2020 depicted that malaria was higher in areas surround to Lake Tana and located to lowlands in the East Gojjam, especially areas border to blue Nile gorge in the region. The spatial variations impacts have varied among months of the year. There were high malaria risks in the region's central and western areas in May and June and shifted to the southwest and northwest areas between August and December. More specifically, districts in the Abay gorge and the Sudan border have a higher malaria risk in Ethiopia's lower and main malaria transmission seasons (Fig. 3b).

Fig. 3.

The estimated partial effects of a three-dimension tensor product of space-time interaction terms, (a) represent smoothed effects of spatial variation through years, (b) represent seasonal variations of malaria transmission across areas of the study regions, and lines display areas with similar smoothed partial effects, northwest Ethiopia, 2012–2020.

4. Discussion

This study demonstrated a spatial-temporal generalized additive model for modeling and evaluating the effects of climate and environmental factors on the monthly malaria cases incidence in the study region. The Space-time effect had a higher contribution in explaining monthly malaria case incidences; however, the influence of climate and environmental parameters is complex and varies according to district and the ecology of vectors. Inclusion of climate and environmental parameters had smaller contribution in explaining the variation of malaria incidence across districts in accounting spatial, temporal, and space-time interaction effects such as seasonality and long-term trends. Malaria incidence has significant seasonality, long-term trend, and spatial variations. The estimated smoothed climate and environmental parameters revealed that they had significant non-linear effects on monthly malaria cases. In addition, space-time interaction effects also significantly explain malaria incidence cases in the study region.

Malaria transmission has seasonal variations, and higher estimated values occurred between September and November following the main rainy seasons between June–September, which is consistent with studying findings in the study region [[5], [6], [7],60], had the lowest effect in February. Malaria transmission has a decreased trend in 2012–2018 and increased after 2018 in which research finding suggests that the stalling of the progress had been due to a limited set of tools and approaches for malaria controlling and elimination and disruptions of health amount of donated to developing countries due to the COVID-19 pandemic [2]. Malaria transmission has spatial variations, and areas with an altitude less than 2000 m are malaria-prone; however, research suggests that malaria transmission expanded to highlands due to global warming, especially in East Africa [12,14,60,61].

Malaria distribution has disparity across districts of the study regions and areas in the Abay Gorge, close to the Benishangul-Gumuz region and near the South Sudan and Sudan border had a higher spatial effect and malaria transmission in 2012–2020. Research findings are consistent with research conducted in the northwest parts of Ethiopia, indicating that districts in westren and northwestern parts of the Amhara region had higher malaria transmission levels [8,10]. Annual and seasonal malaria cases have been varied across areas in the study region. Malaria transmission had seasonal variation across areas where western and northwestern parts of the study region had higher seasonal effects between September and December. However, seasonal variations varied throughout the months, especially in the unstable malaria transmission season between January and June [6,7]. Further, spatial variation of malaria cases changed throughout the study years and followed the patterns of malaria incidences trends, with a decreased estimated value between 2012 and 2018 and an increase since 2019.

Global warming exacerbates the expansion of infectious diseases, and climate effects are complex due to the interplay of several factors. The finding of this study suggests climate and environmental parameters have a significant nonlinear impact on spatiotemporal malaria incidence in areas in northwest Ethiopia. However, the contribution of climate parameters in explaining malaria transmission was smaller than spatial and temporal variations, which contradicts the study finding that suggests a strong relationship between malaria and climate variables like rainfall, minimum, and maximum temperature, and enhanced vegetation index, in which they did not include consider spatio-temporal autocorrelations [5,14,15]. The deviation of the finding might be model differences where most studies did not account for spatial and temporal autocorrelation of climate and environmental predictors, which is essential because they significantly increase the prediction accuracy of malaria transmission. Meanwhile, the malaria transmission encouraging ranges of rainfall, minimum temperature, and maximum temperature was consistent with research findings suggesting that malaria transmission is associated with climate variability [5,6,8]. The favorable ranges of landsurface temperature were found to be with in 15–25 °C in the region. However, the malaria transmission favorable ranges of temperature were changed with types of malaria species, study sites and other environmental factors [14,15,62]. Carlson et al. [63], found that the suitability metric for all four mosquito parasite pairs is predicted to peak at approximately 25 °C [62]; but, the suitability range varies with mosquito parasite, and a study revealed that the transmissibility of malaria is constrained between 17 and 34 °C, which will therefore limit the spatial distribution of malaria on the landscape [14]. The precision of measurements such as the spatial resolution of satellite-derived data and unit of analysis such as point or areal level ranging from village to regional would impact significant relationship and direction. Further, the climate change effect is debatable on malaria transmission, which is varied through landscape change, land cover change, altitudinal variation, and study periods [14]. This study finding is essential since we used the spatiotemporal GAM model for explaining and estimating seasonal and long-term trend variation across areas of the study regions with the account of spatial and temporal autocorrelations. This study evaluated the immediate effects of climate and environmental predictors. Thus, building a predictive model with immediate and delayed effect of climate predictors is required for early warning of malaria transmission at space and time dimensions in-demand by the concerned bodies, which is considered as the limitation of this study.

5. Conclusion

This study used a spatiotemporal generalized additive model to estimate seasonality, trend, spatial variations, and smoothed effects of climate and environmental predictors on the spatiotemporal distribution of malaria cases. Spatial and temporal effects had a higher contribution in explaining the variability of malaria transmission across areas in the study region. Malaria transmission has seasonal variation, and higher seasonal effects occur between September and December. Malaria cases have a decreased trend between 2012 and 2018 and increased since 2019. The space-time effects substantially impact the spatiotemporal variability of malaria cases incidence, and spatial variations were changed through seasons and years. Further, climate and environmental predictors had significant nonlinear effect, but their contributions were smaller in explaining the space-time variation of malaria incidence in the study region. Thus, space-time prediction of malaria cases is required for earning warning systems that alert concerned bodies about an outbreak of malaria transmissions, which enables achieving the WHO milestone in the region and at the national level.

Author contribution statement

Teshager Zerihun Nigussie, Temesgen T. Zewotir, Essey Kebede Muluneh: Conceived and designed the experiments; Analyzed and interpreted the data; Wrote the paper.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

Data will be made available on request.

Declaration of interest's statement

The authors declare no competing interests.

Appendix A. Supplementary data

The following is the supplementary data related to this article: