Predicting the Path of Insurgency: Data-Driven Strategies to Counter Boko Haram in Nigeria

1.1 The Origin of Boko Haram Sect in Nigeria

Boko Haram, which translates as ‘Western education is a sin’, was founded in 2002 in Maiduguri, the capital of Borno state in North-Eastern Nigeria, under the leadership of Mohammed Yusuf. Mohammed Yusuf preyed on disillusioned youth who felt neglected by the government. He offered them hope through religious ideology, painting a clear picture of an enemy to blame for their hardships. Yusuf himself had once been an Almajiri, a religious student forced to beg on the streets to survive (Albert, 2017). By the early 2000s, Yusuf had become a vocal critic of Western education in Nigeria. He blamed the British colonial system, which set up the education system, for the country’s social problems and corruption. Between 2005 and 2009, Yusuf founded a religious group in Maiduguri that later became known as Boko Haram. This group, which attracted a large following of mostly poor Islamic school children, university students, clerics and unemployed youth, lived in a communal compound. On 20 February 2009, Yusuf’s group clashed with the state police, resulting in a deadly confrontation that claimed the lives of several of its members (Adisa, 2021). A series of reprisal attacks and police raids in the following months further escalated tensions. Police raided Yusuf’s cattle farm and Boko Haram’s headquarters, sparking reprisals. The sect launched attacks on military and paramilitary personnel and civilians. In response, a joint military and paramilitary task force captured Mohammed Yusuf. Denied due process, the Nigerian police extra-judicially executed Yusuf outside the station. This brutal act further radicalized the group. Boko Haram splintered and went underground, only to re-emerge in 2011 under Yusuf’s former deputy, Abubakar Shekau. Boko Haram transformed from a religious sect into a full-fledged terrorist organization, waging a bloody insurgency that has devastated Nigeria. To date, the group’s violence is estimated to have killed 38,000 people and displaced millions (Elkaim, 2024).

Boko Haram’s insurgency unfolded in brutal stages. First, they launched sporadic attacks on security forces. Their violence then escalated to target Christians in churches and Muslims in mosques, as well as schools, public gatherings and other civilian locations. The group escalated its brutality, using tactics such as improvised explosive devices (IEDs) and suicide bombings (Adesoji, 2019; Hentz, 2018 and Levan, 2018). In a few short years, Boko Haram has unleashed a wave of terror across North-Eastern Nigeria, carrying out 1,639 violent attacks. This reign of violence resulted in a terrifying human cost: over 14,436 lives lost, 6,051 wounded, and a staggering 2,063 people taken hostage (Botha & Abdile, 2019). Defeating Boko Haram remains a daunting task. The group’s anonymous leadership, characterized by inflexibility and brutality, remains a significant threat. Its tactics are often shrouded in secrecy and its strategic goals remain unpredictable, making it a difficult adversary to counter (Zenn, 2018 and Zenn et al., 2013).

1.2 The Effect of Boko Haram’s Insurgency Impacts to Lives

Boko Haram’s insurgency has had a devastating human cost, with countless lives lost and entire communities displaced. Despite the valiant efforts of the Nigerian Armed Forces, Community Armed Security Personnel and the Joint Task Force, the group has retained a disturbing ability to carry out attacks, including bombings, cattle rustling, kidnappings and killings. These acts of terror, along with rampant sexual and gender-based violence (PGBV), have recently plagued northern Nigeria and the Lake Chad region. This violence has exacerbated the harsh realities of the region, which already faces difficult climatic conditions (Sampson, 2015). Food production and economic activity have been severely disrupted, as the region serves as a major agricultural hub for Nigeria and its neighbours. The insurgency has plunged many into destitution and poverty. Entire villages have been wiped out and vital infrastructure, including schools and social services, destroyed. Hundreds of educational institutions, from primary to tertiary level, have been left in ruins (Maza et al., 2020 and Adisa, 2021). Recently, on Monday, June 24, 2024, Nigeria’s academic community was struck by tragedy when bandits murdered Professor Yusuf Saidu, the deputy vice chancellor for research, innovation and development at the Usmanu Danfodiyo University in Sokoto. Saidu was reportedly travelling on a highway linking Kaduna and Sokoto states when he was attacked by Boko Haram bandits, who were fleeing from the joint military task force (Qosim, 2024). On the 29th of June 2024, a horrific incident occurred in Borno, Nigeria, when a female suicide bomber detonated explosives during a wedding ceremony, killing a large number of happy attendees (Sofia and Chris, 2024). The bombing, one of several that day, drew attention to the ongoing security risks in the region. This episode underlines the ongoing security problems in northern Nigeria, where banditry remains a serious threat.

The Boko Haram insurgency has triggered a massive displacement crisis across the region.

The insurgency has led to the internal displacement of millions of Nigerians. Amnesty International reports that more than 2 million people have been internally displaced in northern Nigeria since the conflict began in 2017 (Omenma, 2019; Onapajo & Uzodike, 2012 and Lar, 2019). The violence has also spilled across borders, creating a refugee crisis in neighbouring countries. The conflict in north-eastern Nigeria has caused a significant refugee crisis, with over 170,000 Nigerians seeking asylum in Cameroon, Niger and Chad (Sani et al., 2018). An estimated 82,260 people in the Lake Chad region, 192,912 people in the northern region of Cameroon and 184,230 people in Niger have been displaced from their homes; forced to flee violence (Iocchi, 2018). The security situation in Nigeria remains volatile, fuelling a widespread sense of insecurity among the youth. This has led many young, productive Nigerians to embrace the concept of ‘japa’ - migration to countries perceived to be safer. This exodus of skilled workers and intellectuals has a ripple effect on the Nigerian economy: the workforce shrinks and the nation loses the potential contributions of these individuals. In addition, fear of kidnapping or violence by both Boko Haram and Fulani herdsmen, who see the group as an extension of themselves, has led to a drastic decline in agricultural activity. This has led to food shortages and inflation of essential goods. To combat Boko Haram effectively in the short and long term, both the Nigerian government and international bodies need to adopt a multi-pronged approach. While military action may be necessary, it is crucial to develop a comprehensive strategy that addresses the root causes of the insurgency.

This study aims to contribute to such a strategy by proposing essential statistical monitoring tools. By tracking Boko Haram’s activities across the country, including states affected, vulnerable regions, attack rates, casualties and deaths, we can predict future attacks and enable a more proactive response. Monitoring these statistics, including casualties among civilians, security forces and Boko Haram itself, will provide critical insights for planning and defeating the insurgency. Accurate data is the cornerstone of effective action.

2.1 Data source

This study primarily utilized data from the Nigerian Security Tracker (NST) website (https://www.cfr.org/nigeria/nigeria-security-tracker/p29483) covering the period from 2011 to 2023. The NST data was chosen for its high precision and comprehensive coverage of security incidents in Nigeria. Additionally, the analysis incorporated geolocated information on Boko Haram activity obtained from government and international organizations. To improve data reliability and efficiency, the analysis was exclusively carried out using NST data. This dataset was selected for its high precision and comprehensive coverage, including four years of published NDHS data.

2.2 Ethical statement

The data used in this research was extracted from the publicly available Nigerian Security Tracker website (https://www.cfr.org/nigeria/nigeria-security-tracker/p29483). No private information were accessed. Although the data is from a public website, to ensure responsible use of the data, the research protocol received ethical approval from the Research Committee of the Faculty of Physical Sciences, Ambrose Alli University, Ekpoma, Edo State, Nigeria on 9 January 2024. The Nigerian Security Tracker is not a social media platform but a public data platform. We acknowledge the potential ethical considerations associated with the use of publicly available data, particularly the potential for unintentional identification or bias.

2.3 Time series analysis

This study uses the Pucheta et al. (2019) Box-Jenkins methods, a well-established iterative approach for time series analysis. This method involves several steps: first, identification of the model through analysis of the autocorrelation function (ACF); partial autocorrelation function (PACF) and extended autocorrelation function (EACF). Next, the method estimates the parameters using the Maximum Likelihood Estimator (MLE), and finally diagnostic tests are performed to ensure the accuracy of the model.

2.4 Autoregressive Integrated Moving Average (ARIMA) and Seasonal Autoregressive Integrated Moving Average (SARIMA) Models

Within the Box-Jenkins framework, this study uses two specific types of models: Autoregressive Integrated Moving Average (ARIMA) and Seasonal ARIMA (SARIMA). The ARIMA (p, d, q) with zero mean can be expressed as

The SARIMA (p, d, q) (P, D, Q) s model with a mean of zero can be expressed as:

In this study, a combination of techniques is used to ensure that the chosen model accurately represents the data and has strong predictive capabilities. The Augmented Dickey-Fuller (ADF) test Elsayir (2018) is used to check the stationarity of the data. The Box-Cox transformation plot of Ali and Shareef (2023) is used to identify any necessary transformations to achieve normality in the data, which is often desirable for good self-fitting and can improve forecasting accuracy. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are used to compare different candidate models (Silverman, 2019 and Kornreich, 2016). The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are calculated to assess the predictive accuracy of the model (Chai and Draxler, 2014), which can be expressed as:

2.5 Exponential Weighted Moving Average (EWMA) chart

To monitor the activities of Boko Haram, the study also uses a statistical quality control tool known as the Exponentially Weighted Moving Average (EWMA) control chart. The EWMA control chart statistic is defined in Alevizakos et al. (2024) and Aslam et al. (2023). The EWMA Upper Control Limit (UCL), Centre Line (CL) and Lower Control Limit (LCL), defined as:

3.1 Boko-Haram Monthly Death Toll and Insurgency

Tables 1 and 2 examine the total number of death tolls that resulted from Boko Haram Insurgency from 2011 to 2023. The variable ‘deaths’ shows significant variation, ranging from a minimum of 59 to a maximum of 3456 deaths per month. These statistics provide insight into the dynamics of Boko Haram’s activities and the associated toll on human lives and societal stability. The analysis also identified the North East region as the epicentre of Boko Haram activity, with the highest number of deaths. Within the Northeast, Borno State emerged as the area most affected by the insurgency, with the highest number of fatalities. Other states such as: Sokoto, Kaduna, Benue, Adamawa, Plateau, Yobe, Niger, Niger, Katsina, Taraba, Kano, Nasarawa, Zamfara, Kogi, FCT, Gombe, Kebbi, Kwara, Jigawa and Gombe also experienced violence, albeit to a lesser extent.

The time series plot of monthly Boko-Haram and insurgency fatalities is shown in Figure 2. Figure 2 shows the monthly trend of Boko Haram’s monthly insurgency and death toll from June 2011 to June 2023, with 2014 and 2015 as the peak years of their activities. The Box-Cox test identified a log transformation (lambda close to zero) for the Boko Haram monthly death toll data to achieve normality, while the insurgency data remained untransformed (lambda close to one). The ADF test assessed the stationarity of both the transformed death toll data and the insurgency data. The insurgency data was found to be stationary (ADF statistic = -3.7384, p-value = 0.0240). Although the death toll data was not initially stationary (ADF statistic = -3.3735, p-value = 0.0618), it became stationary after the first difference (ADF statistic = -6.4545, p-value = 0.01).

Figure 2. Trends of Boko-Haram Death-Toll and Insurgencies in Nigeria (2011-2023).

Figure 3 shows the ACF and PACF plots used to select the preliminary models for both the transformed death and insurgency data.

Figure 3. ACF and PACF plots for Boko-Haram Insurgency and Death-Toll.

From 3, analysis of the ACF and PACF plots for the log-transformed Boko Haram death toll data revealed a decaying ACF and a PACF with a cut-off after lag 2, suggesting an ARIMA (2,1,0) model as a preliminary choice. Similarly, for the Boko Haram insurgency data, the ACF showed a decaying pattern and the PACF had a cut-off after lag 1, suggesting an ARIMA (1,1,0) model as a possible candidate.

To strengthen the reliability of the models, the Extended Autocorrelation Function (EACF) method is used for further validation, as shown in Table 3.

The EACF indicates that the ARIMA (1, 1, 1) model is the best for the two datasets.

From Table 4, the AIC and BIC are used to select the best model. The RMSE is used as a criterion to check the prediction performance.

Table 4 shows the optimal models for each dataset based on the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). For the Boko Haram monthly death toll data, the SARIMA (0,1,1)(0,0,1)12 model stands out as having the lowest AIC and BIC values among the models compared. The ARIMA(0,1,2) model is selected for the Boko Haram monthly insurgency data as it has the lowest AIC and BIC values compared to the other models considered.

3.1.1 Estimation of the Model Parameters

Table 5 shows the coefficients estimated by maximum likelihood estimation (MLE) for the SARIMA (0, 1, 1) (0, 0, 2)12 model. These coefficients provide an insight into the relationships between the different components of the model and their respective impact on the time series data.

The results in Table 5 show that all coefficients within both models are statistically significant at the 5% level (p <0.05), based on t-tests.

3.1.2 Model Residual Analysis

The Ljung test statistics (X² = 0.5247, df = 1, p-value = 0.4688) for the ARIMA(0,1,1)(0,0,1)₁₂ model (Boko-Haram monthly fatalities) and (X² = 0. 0117, df = 1, p-value = 0.9139) for the ARIMA(0,1,2) model (Boko-Haram monthly insurgency), both indicate a lack of significant autocorrelation in the residuals.

To complement these tests, examining the histogram in Figure 4 allows a visual inspection of the residual distribution. Figure 4 shows that the residuals of the model are approximately normal, suggesting a normal distribution. This supports the assumption that the residuals are normally distributed. The models are therefore good fit for the data sets.

Figure 4. ACF and histogram plots of model residuals.

3.2 Out-of-Sample Prediction or Forecasting

Out-of-sample prediction/forecasts of insurgency and deaths caused by Boko Haram activities for a period of 12 months are generated using the two models as depicted in 5. Figure 5 suggests a potentially lower frequency of Boko Haram insurgency incidents in Nigeria, with an average of about nine attacks per month. This predicted decrease could lead to a reduction in casualties compared to periods of heightened insurgent activity, in line with predicted fatalities.

Figure 5. Boko-Haram monthly insurgency and death-toll model forecasts.

The bar graphs in Figure 6 show the trend in fatalities over the course of the Boko Haram insurgency.

Figure 6. Boko-Haram Insurgency and Death-Toll Bar Plots.