Forecasting malaria incidence in a resource-limited urban setting with climate variables as exogenous regressors: time series analysis using a SARIMAX model in Bahir Dar, Ethiopia

Abstract

Background

Ethiopia has been faced with the continual resurgence of malaria. It affects the health of the young workforce, which is believed to affect and slow economic growth.

Objective

Analyze and forecast the incidence of malaria in the next years (2026–2030) on the basis of historical data from Bahir Dar city in the Amhara National Regional State of Ethiopia.

Methods

A forecasting framework—seasonal autoregressive integrated moving average with exogenous factors (SARIMAX) model—was developed using malaria data from Amhara regional health bureau and exogenous regressors, weather data, from World Weather Online. The dataset comprising 90 monthly data points, spanning from January 1, 2018 to June 30, 2025, was split to develop and validate the model, reserving the first 80% (January 1, 2018–December 31, 2023) for training the model and the final 20% (January 1, 2024–June 30, 2025) for testing forecasting performance. We used the fitted model to forecast for the next 5 years using Python version 3.11.

Results

The SARIMAX (1, 2, 2) (1, 2, 2, 12, exog) model, with weather data as exogenous regressors, fit the historical data well. It revealed an increasing trend, as evidenced by the in-sample fit, out-of-sample forecast and future prediction values, which consistently increased over the prediction horizon. None of the weather condition data showed a statistically significant predictive relationship with malaria incidence (p > 0.05). The evaluation metrics, mean absolute percentage error (MAPE), confirmed reasonable predictive accuracy (28.3%).

Conclusion

Our study demonstrates an upward trend in forecasted malaria cases for the upcoming years, suggesting a potential breakdown in current strategies. The result underscores the necessity of a targeted, localized early warning system to manage resource allocation.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12936-026-05823-1.

Introduction

The global incidence of malaria has decreased sharply in the past 30 years [1]. Despite this fact, it remains one of the most worrisome vector-borne infectious diseases affecting sub-Saharan Africa [2], and since 2020, progress has stopped and, in some sub-Saharan African areas, reversed [1]. Malaria has historically been endemic throughout Ethiopia, posing a significant health risk to its population [3, 4]. Since the middle of the Emperor Haile–Selassie regime (1958), several malaria epidemics have occurred in Ethiopia in most lowland and some highland areas [5]. In line with these challenges, in March 1966, systematic malaria eradication operations began in Ethiopia, with the ambitious goal of eliminating malaria from the country by 1980, which was part of the global initiative efforts led by the World Health Organization (WHO) to eradicate malaria worldwide [6, 7].

In line with the UN SDG plan, the WHO’s new Global Technical Strategy for malaria sets a goal against malaria to “reduce malaria mortality rates and clinical case incidence globally by at least 90% compared with 2015” [8]. Ethiopia has adopted the global technical strategy (GTS) 2025 goals and targets “to reduce both malaria mortality and incidence rates globally by at least 40, 75 and 90%, respectively, by 2020, 2025, and 2030 compared with 2015” [9]. Ethiopia’s current malaria control actions are guided by its National Malaria Elimination Strategic Plan (2021/22–2025/26), which aims to achieve nationwide elimination by 2030. Key actions focus on integrated vector control, prompt case management, and strengthening surveillance systems, implemented by the Ministry of Health and partners [10].

Despite these efforts, the ever-increasing morbidity and mortality due to malaria remain among the most important public health threats, especially in sub-Saharan Africa [11, 12]. In contrast to the ambitious plans, the number of malaria cases has steadily increased since 2020, and most of this increase has occurred in countries in the WHO African Region (89.7%), including Ethiopia, which is one of the main countries contributing to the increase [13]. The reports of national and international authorities from 2021 to 2023 reflect increasing malaria incidence in Ethiopia since 2021 [13, 14].

While a significant progress has been achieved thus far, malaria remains a formidable public health challenge, particularly in the SSA region, including Ethiopia [15]. According to the World Malaria Report 2023, the global malaria case incidence is off track by 55% compared with the global technical strategy milestones [16]. It also continues to pose a significant public health and socioeconomic challenge in Ethiopia despite efforts to eliminate malaria by 2030 [17, 18]. Despite the decreasing trend from 2004 to 2018, Ethiopia is facing an increasing trend of malaria cases from 2021 to 2024 [12, 19, 20]. This recent increase in malaria cases in Ethiopia is attributed to several gaps and challenges in existing strategies, primarily relating to programmatic disruptions, the emergence of insecticide and drug resistance, weak surveillance systems, and a lack of tailored interventions for specific populations [21]. This malaria forecasting is critical in Bahir Dar due to its unique high-risk, wetland-adjacent location, where 80% of the city has high-to-very-high risk [22].

Traditional monitoring methods often struggle to capture these dynamic patterns, creating a critical need for advanced analytical tools. Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX) model provides the most effective and insightful results for short-term forecasting task due to its ability to seamlessly integrate and explicitly measure the impact of external factors. It’s interpretable, statistically grounded nature and our time series data size also made it the superior choice for our specific requirements. A significant positive association has been found between weather conditions and malaria incidence, but often at different lag months [23, 24]. In addition, the SARIMAX modeling framework holds significant practical importance in malaria forecasting by bridging the gap between historical disease trends and external environmental factors. It allows public health officials to move from reactive measures to proactive, data-driven interventions, particularly in high-burden regions. Cognizantly, we performed a time series analysis using SARIMAX model that offers a powerful, data-driven approach to model historical trends and forecast future malaria incidence in Bahir Dar city. Enabling precise predictions is essential in informing proactive public health strategies, optimizing resource allocation, and developing targeted interventions to control and ultimately eliminate malaria.

Methods

Study setting and participants

Bahir Dar is located in the Amhara National Regional State, bordering Lake Tana, where the Blue Nile originated. Malaria is a significant public health concern in Bahir Dar city, Ethiopia, particularly in areas surrounding the wetlands of Lake Tana [25]. The wetlands around Lake Tana are known to be hotspots for malaria transmission, and malaria transmission is seasonal. The city and the Amhara Region saw a progressive decline in malaria cases from 2014 to 2018, followed by a sharp increase, or resurgence, from late 2018 through 2024, reaching the highest levels in a decade [26].

The monthly historical malaria data entered into the model were collected from the Amhara National Regional State Health Bureau archives on August 10, 2025, and the maximum monthly temperature recordings were obtained from WorldWeatherOnline.com (https://www.worldweatheronline.com/) [27] with permission on July 13, 2025, for a seven-and-a half-year period (January 2018–June 2025).

A monthly population denominator data is not available for Bahir Dar city unless we interpolate but from our historical malaria data for the seven and half years (from January 1, 2018 to June 30, 2025), a minimum of 25% and above annual malaria cases increase is observed which is far higher than the 5–7% urbanization rate [28] in the city implying that the intensity of malaria transmission is growing roughly 3–5 times faster than the population itself reflecting unparalleled malaria cases increase.

Study design

Our study employs a retrospective time series analysis to investigate malaria case trends and predict future outbreaks. The design focuses on analyzing historical malaria case data alongside potential influencing factors including nine monthly weather condition variables over seven and a half years. Our primary objective is predicting malaria to provide accurate, timely forecasts of future malaria case incidence in Bahir Dar city, Amhara National Regional State, Ethiopia. The secondary objective was to determine the influence of weather conditions on the incidence of malaria within the study area. This study uses a forecasting framework that applies a seasonal autoregressive integrated moving average with exogenous regressors (SARIMAX) model to forecast the incidence of malaria over the next five years (2026–2030).

Sample size determination

The study population included all malaria-positive cases seen from January 01, 2018, to June 30, 2025, in the Bahir Dar city administration of the Amhara National Regional State. Bahir Dar has a mix of public and private healthcare institutions, including three public hospitals, four private hospitals, ten health centers and fifteen health posts. The time period selected for this analysis runs from January 01, 2018 to June 30, 2025, providing a total of ninety observations recorded at a monthly frequency. Consistent and high-quality data for the endogenous variable, monthly malaria cases data, was only reliably available starting from January 01, 2018. All malaria-positive cases, confirmed through microscopic examination of blood films or Rapid Diagnostic Tests (RDTs), were included. The data were checked for missing values with the intention of addressing them through deletion, imputation (filling in missing values), or model-based approaches, depending on the amount and pattern of missing data, and were found to be clean and complete for the specified period.

Diagnosis, classification and operational definitions:

Positive malaria cases: the presence of disease caused by Plasmodium parasites in a patient’s blood through a quality-controlled microscopic blood smear examination or a rapid diagnostic test (RDT) [29].

Data management/analysis

Data analysis was performed via Python version 3.11 with libraries including but not limited to pandas for data manipulation; NumPy for numerical operations; matplotlib for visualization; Statsmodels to explore data, estimate statistical models, and conduct statistical tests; seaborn for data visualization; and Scikit-learn for machine learning and statistical modeling to perform data preprocessing, feature selection, and implementation of our predictive model. Python was chosen for its extensive collection of scientific computing libraries and its flexibility in developing complex analytical workflows [30]. Our time series forecasting was executed in six steps:

Data discovery, understanding and preparation

We loaded our dataset into Python version 3.11 to understand the trend, seasonality and other characteristics of our data via both statistical (augmented Dickey‒Fuller test) and visual methods (rolling statistics). The Data were also checked for missing values.

Transforming data for stationarity

Square-root transformation followed by seasonal differencing (second order differencing) is implemented on our non-stationary, non-linear time series data exhibiting both high, changing variance (heteroscedasticity) and a strong, non-linear trend. The square root stabilizes variance, while second-order differencing removes complex, non-linear trends. After applying this second-order differencing (square root transformation followed by seasonal differencing), the time series data was analyzed using rolling statistics with a 12-month window to assess underlying trends and stationarity. A formal statistics test, augmented Dickey-Fuller (ADF) test, of our second-order differenced data was executed to show stationarity.

Model selection and building

Choosing a suitable model

Our study uses the SARIMAX model, as our data have a seasonal pattern, and the monthly weather condition variables across the study period were used as exogenous factors that are expected to affect the target variable, monthly positive malaria cases in Bahir Dar city.

Determining the model parameters

We used autocorrelation function (ACF) and partial autocorrelation function (PACF) plots to determine the p, d, q, P, D, and Q parameters, which, in turn, enable our model to accurately reflect real-world data, leading to reliable prediction. The model parameter “d” refers to the differencing order with which we achieve stationarity. In our case, it is 2, as we achieve stationarity with second-order time series differencing (square root transformation followed by differencing). However, to ensure a more comprehensive search for the optimal model parameter, we explored potential values for each order rather than strictly adhering to the lag values inferred from the plots. We then evaluated the SARIMAX model on the basis of the Akaike information criterion [30] and Bayesian information criterion (BIC) model selection criteria.

Splitting—training—test data

We implemented a chronological splitting of our data into training and test data (80%:20%) for unbiased evaluation of our model’s performance. We randomly partitioned the dataset into training and testing sets using an 80/20 split. The larger training set (80%) was used to fit the parameters of the model, allowing it to learn the underlying patterns and relationships within the data. The remaining testing set (20%), which was held out during the training phase, was then used to evaluate the model’s performance on unseen data. This methodology helps to provide an objective assessment of the model’s generalization capabilities and detect potential issues like overfitting [31].

Fitting the model

This allows us to capture temporal patterns, such as trends, seasonality, and autocorrelation, which are essential for accurate forecasting and understanding the underlying dynamics of the data. The chosen model is trained on the training data.

Forecasting and prediction

We used the fitted model to predict future values on the test set and forecast for the next 5 years.

Interpretation and visualization

The selected model performance was evaluated by comparing the predicted and actual values via the metric mean absolute percentage error (MAPE because of its straightforward interpretability and ability to treat individual errors equally. The forecasted value is visualized by plotting the actual vs. predicted values. Residual analysis was performed to confirm model accuracy.

Results

Data discovery, understanding and preparation

We utilized monthly malaria incidence data of seven and half years from January 01, 2018 to June 30, 2025 for analysis. The collected data were loaded into a suitable data structure (pandas DataFrame) and examined to understand the overall trend and seasonality of malaria in the city using graphical visualization. From 2018 to 2022, the data exhibit a gradual upward trend with clear seasonal fluctuations. However, after 2022, the number of malaria cases in Bahir Dar city rose sharply, becoming persistently high and still maintaining its seasonality, reflecting that malaria incidence is increasing in the city (Fig. 1).

Fig. 1.

Time series plot of the monthly positive malaria cases, Bahir Dar city, 2018–2025

Our cycle plots visualized the seasonal patterns and increasing trends of the original historical malaria incidence data. With the monthly data plot, all the January values are plotted (in chronological order), followed by all the February values, and so on. It visualizes the seasonal patterns within the time series data by extracting and displaying the data for each season separately, providing us insights into how seasonal patterns manifest over time and if there are any major changes across the seasons. Each seasonal sub-series in the cycle plots resembles a mini–line graph, allowing us make a clear visual comparison of the seasonal patterns across a larger period. The horizontal line displayed within each of the mini–line graphs indicate the mean value. Both clearly show seasonality and increasing trend in our data. (Fig. 2).

Fig. 2.

Cycle plot of the monthly positive malaria cases in Bahir Dar city—2018–2025

A multiplicative model seasonal decomposition was applied to the original and differenced time series malaria data consecutively to extract the trend, seasonal and residual components. In the original data, the trend analysis revealed a consistent upward increase in malaria incidence over the seven and half year’s period. A strong annual seasonality was also identified, with peaks consistently occurring in Q2 and Q4. Visual inspection of the residuals plot revealed that most of the data points were centered around zero. However, a notable spike/outlier was observed in the residual series, particularly at around 2019. This significant deviation from the expected pattern suggests the presence of unusual, non-systematic event not explained by the regular trend and seasonal components (Fig. 3).

Fig. 3.

Seasonal decomposition of the monthly positive malaria cases. Original non-stationary data vs. second order difference stationary data

The original time series data was transformed using a second-order differencing operation to achieve stationarity (square-root transformation followed by differencing at lag of 12). Seasonal decomposition was then applied to this transformed data. The trend component from the decomposed data was found to be near zero throughout the series, suggesting a stable rate of change in the original data. The seasonal component exhibited a consistent, repeating pattern with a fixed period of 12 months. This indicates persistent, predictable fluctuations in the acceleration of the original time series at regular intervals. The residual component exhibited a mean near zero and appeared to be randomly distributed. The successful reduction of the residuals to white noise confirms the effectiveness of our second-order differencing in achieving a stationary series for modeling purposes (Fig. 3).

Transforming data for stationarity

Initial analysis of the monthly positive malaria cases time series data revealed significant non-stationary characteristics, confirmed by a non-significant result from the Augmented Dickey-Fuller (ADF) test (ADF statistics = 5.65, p-value = 1). First-order differencing was applied to remove the linear trend; however, residual non-stationarity remained (ADF statistics = 1.12, p-value = 0.99). Consequently, second-order differencing (square root transformation followed by seasonal differencing) was implemented, which successfully removed the remaining pattern and achieved stationarity. The twice-differenced series was then used in the final model. Following this transformation, the ADF test on the transformed series yielded a p-value of 0.007 and ADF statistics = −3.52, below the 0.05 significance threshold, indicating the null hypothesis of non-stationarity was rejected (Table 1).

Table 1.

Summary of the augmented Dickey-Fuller test (ADF test)

Time series data	ADF statistic	p value
Original series/monthly positive malaria cases/	5.646	1
First-order differenced series/cube root transformed/	−0.0031	0.958
Second-order differenced series/cube root transformed shifted/	−3.671	0.0045

Visual inspection of the rolling statistics plots for our original and differenced data supports that both the rolling mean and rolling standard deviation remain relatively constant over time and close to the overall mean and standard deviation after differencing. This provides visual evidence for the achievement of weak stationarity, making the data suitable for time series models that rely on our assumption (Fig. 4).

Fig. 4.

Visual evidence of stationarity: fluctuating vs. smoother rolling statistics for original and second order differenced data

Model selection and building

Choosing a suitable model

We evaluated ARIMA (1, 2, 2), SARIMA (1, 2, 2) (1, 2, 2, 12) and SARIMX (1, 2, 2) (1, 2, 2, 12, exog (weather condition)) models to determine the best fit for the observed data patterns. Model performance was assessed via the Akaike information criterion [30], Bayesian information criterion (BIC), and mean absolute percentage error (MAPE). Table 2 summarizes the performance metrics for each candidate model. Compared with the other models, the SARIMAX (1, 2, 2) (1, 2, 2, 12) model achieved the lowest AIC (75.8) and BIC (101.58) values, as well as the lowest MAPE (28%), indicating superior fit and acceptable predictive accuracy. Its superior performance on the AIC, BIC, and MAPE metrics demonstrates its ability to capture the significant annual seasonality effectively and the underlying trend and autoregressive components identified in the time series data.

Table 2.

Summary of the performance metrics for each candidate model

Model	AIC	BIC	MAPE
ARIMA	1568	1578	44.4%
SARIMA	1126	1141	28.30%
SARIMAX	75.8	101.58	28.30%

Determining the model parameters

After the time series was transformed to ensure stationarity (by second-order differencing, d = 2), the autocorrelation (ACF) and partial autocorrelation (PACF) functions were analyzed. The significant spikes in the ACF and PACF suggested model options for the stationary component. The estimated parameters for the final model were as follows: AR = 0.8 (p-value < 0.01) MA = 0.8 (p-value < 0.05) MA = 0.6 (p-value < 0.01) and MA = 0.55 (p-value < 0.05) (Fig. 5).

Fig. 5.

PACF and ACF of the second order differenced time series monthly malaria data

Splitting—training—test data

The complete historical dataset, spanning from January 1, 2018, to June 30, 2025, was divided to develop and validate the predictive model. A chronological split was performed, reserving the first 80% of the data (January 1, 2018–December 31, 2023) for training the model and the final 20% of the data (January 1, 2024–June 30, 2025) for testing its forecasting performance on unseen future data.

Fitting the model

In the process of fitting the SARIMA model, we first identified the appropriate model order by determining the values of p, d, q, P, D, and Q. Using the augmented Dickey‒Fuller (ADF) test, we assess the degree of differencing required to achieve stationarity on the original time series, first-order differenced series, and second-order differenced series. Second-order differencing was achieved by applying a square root transformation first-order differencing followed by a seasonal differencing operation at a lag of 12 months. On the basis of these results, we set d = 2 and D = 2 in the SARIMA model to achieve stationarity in the time series.

Following this, we determined the autoregressive (AR) order (p), moving average (MA) order (q), seasonal AR order (P), and seasonal MA order (Q) for the SARIMA model. Unlike the differencing parameters (d, D), the selection of p, q, P, and Q was not a strictly rule-based process but rather involved an observation-based empirical judgment. We first examined the ACF and PACF plots of the second-order differenced series of the monthly positive malaria cases. Both the ACF and PACF exhibited a prominent first few spikes. However, to ensure a more comprehensive search for the optimal model parameter, we explored potential values for each order rather than strictly adhering to the lag values inferred from the plots. We then evaluated the SARIMA models on the basis of the Akaike information criterion [30] and Bayesian information criterion (BIC) model selection criteria (Table 3) Finally, we used the SARIMA (1, 2, 2) (1, 2, 2, 12) model as the baseline configuration in the subsequent SARIMAX model, where an exogenous variable is incorporated.

Table 3.

AIC and BIC values for the selected SARIMA models

(p, d, q) (P, D, Q)	AIC	BIC
(1, 2, 2) (1, 2, 2)	75.8	101.58
(1, 2, 1) (1, 2, 1)	119	145.8
(0, 2, 1) (0, 2, 1)	123	146

Forecasting and prediction visualization:

Figure 6 displays the actual values against the fitted (in-sample) and forecasted (out-of-sample) values. Visual inspection confirms that the out-of-sample forecast (green line) is consistent with the in-sample fit (red line), effectively tracking the upward trend observed in the actual data. The alignment between the in-sample and out-of-sample lines suggests that the underlying data generating process remained stable, and the model parameters are robust for future predictions.

Fig. 6.

SARIMAX model training and validation: In-sample fit and out-of-sample forecast

As displayed in Fig. 7, the future forecast extends consistent trajectory, projecting a continuation of the current trends with appropriate widening of the confidence intervals, reflecting the forecasts and observed data are showing a rising number of malaria cases with increased uncertainty further into the future, which aligns with recent trends in some regions.

Fig. 7.

Future malaria incidence forecast with exogenous regressors: SARIMAX model

Residual analysis for model accuracy

The plot of the standardized residuals against the predicted values (Fig. 8) displayed a random scatter of points around the horizontal axis (y = 0), with no discernible patterns confirmed by the absence of patterns in the residual plot and a non-significant Shapiro‒Wilk test (statistics = 1.000, p value = 1.000). This random distribution confirms that the assumption of constant variance (homoscedasticity) is likely met.

Fig. 8.

Residual analysis for model accuracy

Exogenous regressors

After exploring alternative lag structures and reduced variable sets, none of the climate variables, factors often associated with malaria transmission, showed a statistically significant predictive relationship with malaria incidence (p > 0.05) in our study area (Table 4).

Table 4.

Time series regression: exogenous variables’ p-values and level of significance

SARIMAX results
Dep. variable:	y			No. observations:	90
Model:	SARIMAX (1, 2, 2) x (1, 2, 2, 12)			Log Likelihood	−21.903
Date:	Sun, 14 Dec 2025			AIC	75.805
Time:	18:15:24			BIC	101.580
Sample:	02-01-2018			HQIC	84.892
	07-01-2018
Covariance type:	opg
	Coef	Std err	z	P>|z|	[0.025	0.975]
Max temp C	0.1063	0.233	0.457	0.648	−0.350	0.562
Rain in mm	0.2662	0.204	1.303	0.193	−0.134	0.667
wind speed	−0.0820	0.371	−0.221	0.825	−0.809	0.645
Humidity	−0.1424	0.287	−0.497	0.619	−0.704	0.420
Pressure MB	−0.4783	0.255	−1.877	0.061	−0.978	0.021
Cloud cover	−0.3173	0.394	−0.806	0.420	−1.089	0.454
Sun_hour	0.1739	0.234	0.743	0.457	−0.285	0.632
Sun_days	−0.1293	0.326	−0.397	0.691	−0.767	0.509
UV index	0.1729	0.189	0.915	0.360	−0.197	0.543
ar.L1	−0.9613	0.234	−4.107	0.000	−1.420	−0.503
ma.L1	−0.1581	2157.198	−7.33e−05	1.000	−4228.188	4227.872
ma.L2	−0.8419	1816.161	−0.000	1.000	−3560.451	3558.768
ar.S.L12	−0.5252	0.347	−1.516	0.130	−1.204	0.154
ma.S.L12	−0.7261	1037.094	−0.001	0.999	−2033.393	2031.940
ma.S.L24	−0.2741	284.475	-−0.001	0.999	−557.836	557.288
sigma2	0.1391	292.219	0.000	1.000	−572.600	572.879
Ljung-Box (L1) (Q):	0.77			Jarque-Bera (JB):	0.69
Prob(Q):	0.38			Prob(JB):	0.71
Heteroskedasticity (H):	0.82			Skew:	0.32
Prob(H) (two-sided):	0.74			Kurtosis:	2.78

Warnings: (1) Covariance matrix calculated using the outer product of gradients (complex-step)

Discussion

Our analysis displayed an increasing trend in the monthly malaria cases across the in-sample fit, out-of-sample forecast, and future predictions using a SARIMAX (1, 2, 2) (1, 2, 2, 12, exog) model suggesting a significant public health challenge in Bahir Dar city. The pattern and trend of malaria incidence in our study, stretching from January 01, 2018 to June 30, 2025, indicates that, despite existing control efforts, the underlying drivers of malaria transmission are intensifying and are expected to continue doing so similar to most sub-Saharan African countries [32, 33]. In addition, our study showed that malaria cases in Bahir Dar show a distinct seasonal trend, with peaks occurring during the pre-rainy (June–July) and post-rainy (October–November) periods [34]. This seasonal peaks in malaria cases are driven by a combination of climatic factors that create ideal conditions for the breeding, survival, and transmission capabilities of the Anopheles mosquito vectors, coupled with human behavioral factors [35, 36].

The in-sample fit, reflecting an increasing trend, indicates that the historical data already contains a strong, persistent upward trajectory that the model has effectively captured. This suggests that the dynamics driving malaria incidence were already in place during the observation period and the model has successfully identified this long-term movement, suggesting that the dynamics influencing malaria incidence were consistent enough for the model to learn and replicate the pattern [37].

The out-of-sample forecast also shows an increasing trend that aligns with the available recent actual data and the in-sample fit. It suggests that the model is robust in capturing the underlying trend and seasonal patterns. This evidence from the out-of-sample performance is more trustworthy for real-world application for the successful forecast and practical utility [38, 39].

The future predictions that extend the upward slope highlight a significant public health concern [40]. The widening confidence interval as time progresses reflects that the forecast becomes increasingly uncertain the further, we predict into the future. A widening confidence interval is a normal and expected feature of time series forecasting because of compounded uncertainty, inherent randomness and model limitations [41]. This up surge might be partly explained by but not limited to Bahir Dar’s proximity to the wetlands of Lake Tana that makes it a malaria hotspot, with the wetlands providing extensive breeding habitats for mosquitoes, decrease in operational vigilance following earlier successes, a phenomenon termed the “elimination-resurgence paradox”, Socio-political Instability and Plasmodium vivax Dominance [26].

Based on our future predictions, the city is likely to face a growing burden of malaria cases, which will strain healthcare systems and resources [42]. This indicates a need for urgent review and potential redirection of existing malaria control strategies.

The exogenous regressors temperature, rainfall, wind speed, humidity, pressure, cloud cover, number of sunny hours and the UV index were found to be statistically insignificant predictors of malaria incidence in Bahir Dar city. This lack of significance might indicate that the relationship between the exogenous variables and malaria incidence is not simple or linear or that its effects are more nuanced than those captured by the statistical model used [43]. Instead of acting as a sole driver, weather conditions may act as one factor within a larger, multivariate system that includes crucial non-climatic influencers, including but not limited to socioeconomic conditions and public health interventions [44]. The time series trend may also be driven by factors not adequately captured by the chosen climatic variables (or their specified lag times). These could include socioeconomic changes, land use modifications, population density shifts, urbanization, the effectiveness of healthcare interventions, drug resistance in parasites, or insecticide resistance in vectors [45, 46]. The study period covered only seven and half years and, thus, was too brief to evaluate the potential effects of global warming on vector distribution and on malaria incidence [44]. The climate variables and geographic specifics might also influence malaria with different, un-tested lag times and regions [47]. If climate variables are insignificant, it does not necessarily mean they are irrelevant. It usually indicates that in the specific, localized, and temporal context, human-driven interventions and non-linear interactions are stronger determinants of the current, observed malaria trends [48].

When evaluated on the test set, the model achieved a mean absolute percentage error (MAPE) of 28.3%, representing a moderate level of predictive accuracy, indicating that on average, forecasts deviate from actual cases by nearly 28% [49]. While this suggests the model captures general trends, such uncertainty means the model is better suited for trend prediction, like cases are rising, rather than precise numerical forecasting. In summary, a 28.3% MAPE means the model is a valuable tool for strategic anticipation but requires a buffer in resource planning to account for the moderate uncertainty. That aligns with early-warning needs by providing a functional, albeit moderate, level of predictive accuracy that enables proactive public health responses, especially in high-burden areas like Bahir Dar city, provided that decision-makers are aware of the associated uncertainty and use the warnings as one piece of the overall surveillance picture.

Residual analysis confirmed that the model residuals approximate white noise [50], suggesting a well-fit model confirmed by the absence of patterns in the residual plot and a non-significant Shapiro‒Wilk test (statistics = 1.000, p value = 1.000), reflecting that residuals are random, uncorrelated, and without patterns [51]. Our predictions also closely track the actual observed values, demonstrating the model’s ability to mirror real-world outcomes.

This SARIMAX model analysis demonstrates the potential for acceptable accuracy, near-term malaria forecasting, which is critical for enhancing Malaria Early Warning Systems (MEWSs). The predictive capability of the model, validated against observed data, allows public health officials to anticipate increases in malaria risk. This knowledge provides a robust foundation for public health officials to forecast future malaria outbreaks and enables proactive interventions. Such timely and targeted responses can significantly improve the effectiveness of malaria control efforts and ultimately lead to a reduction in disease burden.

In conclusion, our analysis indicates a persistent public health challenge where the increasing malaria burden is primarily shaped by non-climatic influences, demanding a comprehensive, integrated approach to interventions beyond climate-focused strategies. In addition, we recommend further studies that focus on alternative predictors and modeling strategies to improve malaria prediction and identify other possible predictors including integration of non-climatic drivers, spatial heterogeneity, and nonlinear modelling approaches.

Conclusion

The developed SARIMAX model effectively captured inherent malaria incidence patterns but found selected exogenous variables statistically insignificant. Forecasts show a concerning upward trend predominantly driven by uncaptured epidemiological factors necessitating the urgent implementation of an early warning system that integrates forecasting with, proactive, targeted interventions.

Limitations of the study

As we are using data from a single meteorological station, this finding cannot represent a large, geographically diverse district, as climatic variables can fluctuate over small distances. In addition, our single location finding cannot be easily generalizable to other areas, even those with similar altitudes or latitudes, because local ecological and social conditions vary widely.

While the SARIMAX model provided reasonable accuracy, models that work well in one location may not be applicable to another due to geographical and epidemiological differences and malaria transmission involves complex non-linear dynamics, which can be challenging for traditional linear time series models to capture accurately.

Our time series model did not reveal a significant association between exogenous regressors and malaria incidence in Bahir Dar city. However, these findings should be interpreted with caution because of the complex relationships among various factors, including non-climatic variables.

The model’s predictive accuracy is limited as insignificant exogenous variables can introduce more “unknowns” and noise into the forecasting process, potentially worsening prediction accuracy compared to a simpler univariate model.

Long-term forecasting inherently faces significant challenges due to accumulating uncertainties, which are quantitatively reflected in widening confidence intervals (CIs).

Abbreviations

ACF

Auto-correlation function

ADF

Augmented Dickey‒Fuller test

AIC

Akaike information criterion

AR

Auto-regressive

ARIMA

Auto-regressive integrated moving average

BIC

Bayesian information criterion

GTS

Global technical strategy

MA

Moving average

MAPE

Mean absolute percentage error

MEWS

Malaria early warning systems

PACF

Partial auto-correlation function

SARIMA

Seasonal auto-regressive integrated moving average

SARIMAX

Seasonal auto-regressive integrated moving average with exogenous factors

SDG

Sustained development goal

UN

United Nations

WHO

World Health Organization

Author contributions

TT: study design; data acquisition, analysis, and interpretation; contributed to the choice of analytical tools; project administration; supervision and wrote the initial draft of the manuscript. MA: study design; data acquisition, analysis, and interpretation; contributed to the choice of analytical tools and participated in the analysis and interpretation of the results. Both authors made substantial contributions to the content and approved the final version. Both authors have agreed to be personally accountable for the author’s own contributions and to ensure that questions related to the accuracy or integrity of any part of the work..

Funding

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

Data availability

The data used for this study are available in the supporting information of this article. The malaria data were obtained from the Amhara National Regional State Health Bureau with permission. Weather data were obtained from WorldWeatherOnline.com with permission. Weather data are available at (URL: https://www.worldweatheronline.com).

Code availability

The code used for data analysis is available from the corresponding author upon reasonable request.

Material availability

The materials that support this study are available in the supporting information of this article.

Declarations

Ethics approval and consent to participate

Ethical approval is not required for this study.

Competing interests

The authors declare no competing interests.