Mikailalsys Journal of Mathematics and Statistics

Utilizing Permutation and Combination Techniques in Business Decision-Making Processes

2026-03-19T09:22:50+08:00

Although permutations and combinations are often regarded as purely theoretical mathematical topics, they play a significant role in practical decision-making and contemporary business operations. This study examines the application of permutations and combinations in everyday decision-making and real business contexts, particularly in quality control, marketing strategy, resource planning, and inventory management. Using real-world examples and case studies, the article demonstrates how organizations employ these combinatorial concepts to improve productivity, reduce costs, optimize available resources, and strengthen competitive advantage in increasingly complex market environments. The findings indicate that a sound understanding of permutations and combinations enhances managerial and executive decision-making, especially when evaluating numerous alternatives, assessing the likelihood of possible outcomes, selecting appropriate combinations of people or products, and determining optimal configurations. The study concludes that permutations and combinations are not merely academic concepts but practical analytical tools that support more effective and strategic business decisions. This study contributes to a broader understanding of how foundational mathematical reasoning can be applied to improve organizational efficiency and decision quality in business practice.

Semi-Analytical Study of Pulsatile Nanofluid Flow in Porous Stenosed Arteries Under Magnetic and Thermal Effects

2026-03-25T08:38:55+08:00

This study presents an extended fractional Maxwell fluid model for pulsatile blood flow through a stenosed artery by incorporating the combined effects of a magnetic field, porous medium, chemical reaction, heat source, and suspended nanoparticles. Blood is modeled as a compressible, viscoelastic, and electrically conducting fluid, and the governing fractional-order coupled nonlinear partial differential equations for momentum, energy, and nanoparticle concentration are formulated in cylindrical coordinates. To capture fluid memory effects, the Caputo fractional derivative is employed, and the resulting system is solved semi-analytically using the Laplace transform method. The inverse Laplace transforms, involving modified Bessel functions, are computed numerically through the Concentrated Matrix-Exponential method implemented in Python to improve stability and accuracy. Validation against existing literature demonstrates excellent agreement. The parametric results show that increasing the Hartmann number, stenosis length, particle mass, and chemical reaction parameter reduces both velocity and nanoparticle concentration, whereas higher heat source, Peclet number, and nanoparticle concentration parameters enhance flow and particle dispersion. The findings further indicate that fractional-order effects strongly influence velocity behavior, with lower fractional orders producing stronger memory effects and smoother gradients. The study concludes that the proposed model improves the prediction of hemodynamic behavior under pathological arterial conditions and offers useful implications for magnetic-assisted therapies and nanoparticle-based drug delivery.

Mathematical Modelling of Kidnapping Activities

2026-03-30T09:20:50+08:00

Kidnapping has become one of the most severe security challenges in Nigeria, particularly in the northern regions, where it has evolved into a profitable criminal enterprise. This study develops a mathematical model to analyze the dynamics and control of kidnapping activities. The population is classified into five compartments: susceptible individuals, exposed individuals, informants, kidnappers, and repentant kidnappers. The model describes the transition of individuals from vulnerability to involvement as informants or kidnappers, as well as the possibility of repentance through rehabilitation. A basic reproduction number, (R_0), is derived to determine whether kidnapping activities will persist or decline. The analysis indicates that kidnapping can be eliminated when (R_0 < 1), whereas (R_0 > 1) implies its continued persistence. Numerical simulations further show that increasing the rehabilitation rate of kidnappers promotes repentance, while strengthening intelligence gathering through informants and reducing recruitment into kidnapping significantly suppress the expansion of this criminal activity. The study concludes that the proposed model provides useful quantitative insight into the mechanisms driving kidnapping and offers practical implications for policy interventions aimed at reducing kidnapping in Nigeria.

Inference and Simulation Study for the Exponentiated Novel α-Power Gumbel Model

2026-03-30T09:43:09+08:00

This study introduces and investigates a new flexible lifetime model, termed the Exponentiated Novel α-Power Gumbel (ENAPG) distribution, by applying the exponentiation technique to the recently proposed novel α-power Gumbel model. The proposed distribution extends the classical Gumbel family through the inclusion of an additional shape parameter, thereby enhancing its flexibility for modeling right-skewed and heavy-tailed data. To establish its theoretical usefulness, the study derives key statistical properties of the ENAPG distribution, including the survival and hazard rate functions, quantile function, moments, moment-generating function, Rényi and Tsallis entropies, and order statistics. Parameter estimation is carried out using the maximum likelihood estimation approach, with the resulting nonlinear likelihood equations solved numerically through iterative optimization routines. A comprehensive Monte Carlo simulation is further conducted to assess the finite-sample performance of the estimators across different sample sizes using bias, mean square error, root mean square error, and mean relative error criteria. The results indicate that the maximum likelihood estimators exhibit consistency and improved efficiency as sample size increases. Overall, the ENAPG distribution provides a robust and flexible alternative to existing Gumbel-type models and offers potential applications in reliability analysis, survival studies, and extreme-value modeling.

Spatial Epidemiology of Lassa Fever in Nigeria: Mapping and Predictive Analytics for Improved Disease Control

2026-03-30T09:59:17+08:00

Lassa fever remains a major public health concern in Nigeria because of its recurrent outbreaks, high morbidity, and fluctuating case fatality rates. This study investigates the geographical distribution and temporal dynamics of Lassa fever in Nigeria from 2020 to 2025 using spatial epidemiology and predictive analytics. Surveillance data obtained from the Nigeria Centre for Disease Control were analyzed through geospatial mapping to visualize confirmed cases and deaths at the state and Local Government Area levels, while Bayesian hierarchical spatial models, specifically the Integrated Nested Laplace Approximation and Besag-York-Mollié models, were applied to generate predictions and identify persistent and emerging hotspots. The findings show that a small cluster of states, particularly Ondo, Edo, and Bauchi, consistently accounted for more than 70% of annual confirmed cases. Case fatality rates ranged from 16% to 21% during the study period, with notable increases in 2023 and 2025. The hotspot maps further reveal marked spatial heterogeneity in disease risk, shaped by ecological suitability for rodent reservoirs, population density, and disparities in health systems. In addition, the predictive outputs show strong agreement with historical data, confirming the usefulness of the models for early warning. The study concludes that integrating spatial mapping with predictive modeling provides a robust framework for strengthening Lassa fever surveillance and response in Nigeria. These findings contribute a scalable and adaptable methodological approach that can support outbreak forecasting, resource optimization, timely intervention in high-risk areas, and broader data-driven epidemic intelligence for infectious disease control.

Small Area Estimation of Child Multidimensional Poverty in Nigeria: A Linear SAE Approximation Using MICS 2021 and WorldPop 2020 Data

2026-05-16T16:39:31+08:00

This study estimates child multidimensional poverty across Nigeria’s 774 Local Government Areas (LGAs) by integrating the 2021 Multiple Indicator Cluster Survey (MICS) with WorldPop 2020 high-resolution population density data. Using the Alkire–Foster framework, the analysis produced a national weighted Multidimensional Poverty Index (MPI) of 0.292 and a raw MPI of 0.23632, based on a poverty incidence value of H = 0.56, which implies approximately 55.7 million children in multidimensional poverty, and an average deprivation intensity of A = 0.422. To generate LGA-level estimates, this study applied the Fay–Herriot small area estimation (SAE) model by regressing MPI on the logarithm of population density, conflict indicators, and infrastructure measures. The model explained more than 80% of the variance, improving the goodness of fit from R² = 0.695. Non-linear specifications were tested but were not retained based on the Akaike Information Criterion (AIC). A logit transformation was applied to bound predictions within a plausible range of 0–0.569, thereby eliminating negative estimates. Uncertainty estimation incorporated MICS sampling variance through bootstrapping, with coefficients of variation below 15% for 90% of LGAs. The findings reveal substantial regional disparities in child multidimensional poverty, with the North West recording a zonal MPI of 0.447 compared with 0.090 in the South East. Although constrained by data limitations, the study demonstrates the utility of SAE for producing granular poverty estimates and contributes to policy-oriented poverty measurement by strengthening evidence for geographically targeted child poverty reduction in Nigeria.

Analysis of Steady Radiative MHD Nanofluid Flow in a Porous Medium: Effects of Magnetic Field, Prandtl Number, and Internal Heat Source/Sink

2026-05-16T16:55:10+08:00

This study presents a numerical investigation of steady magnetohydrodynamic (MHD) nanofluid flow under the combined effects of thermal radiation, Prandtl number, porous medium permeability, magnetic field strength, and internal heat generation or absorption. The objective is to examine how these governing parameters influence velocity profiles, temperature distributions, and surface heat transfer characteristics. The nonlinear partial differential equations describing coupled momentum and energy transport were reduced to a system of dimensionless ordinary differential equations through suitable similarity transformations and solved numerically. The results show that thermal radiation and internal heat generation substantially increase the temperature field, while momentum transport is suppressed due to intensified thermal–magnetic interactions and resistive forces. An increase in the Prandtl number reduces thermal diffusion and produces thinner thermal boundary layers. Higher porous medium permeability introduces porous resistance that decelerates the flow but enhances surface heat transfer through boundary layer thinning. The applied magnetic field also regulates both momentum and thermal transport through Lorentz forces. Mathematically, these trends are consistent with the structure of the dimensionless governing equations and boundary conditions, indicating strong nonlinear coupling among diffusion, convection, radiation, porous drag, and electromagnetic effects. The study concludes that surface heat transfer performance, represented by the Nusselt number, is primarily governed by wall temperature gradients. These findings contribute to the numerical understanding of MHD nanofluid transport in porous media and provide a useful theoretical basis for applications involving thermal regulation and heat transfer enhancement.

Bayesian Hierarchical and Decomposition Analysis of Pregnancy-Related Mortality in Nigeria Using NDHS 2018-2023/24

2026-05-16T17:07:46+08:00

Nigeria continues to face one of the highest burdens of pregnancy-related mortality globally, yet recent measurement evidence remains constrained by gaps in direct reporting. This policy and measurement note examines the availability of direct sibling-history estimates in the Nigeria Demographic and Health Surveys (NDHS), with particular attention to the absence of an updated pregnancy-related mortality ratio (PRMR) in the 2023–24 reporting cycle. The NDHS 2018 reported a national PRMR of 512 per 100,000 live births (95% CI: 447–578). However, the NDHS 2023–24 Key Indicators and Summary Reports do not publish an updated sibling-history-based PRMR, thereby limiting direct assessment of mortality trends. Proxy indicators suggest modest progress, including a decline in the total fertility rate from 5.3 to 4.8 and an increase in skilled birth attendance from 43% to 46%, although rural–urban and zonal disparities persist. Exploratory Bayesian hierarchical modeling using NDHS 2023–24 microdata produced an illustrative national PRMR estimate of approximately 462 per 100,000 live births (CrI: 392–532), suggesting a possible modest decline, while rural estimates remain high at approximately 612. The findings indicate that the absence of a published direct PRMR weakens evidence-based monitoring of SDG 3.1 and limits independent assessment of progress in reducing pregnancy-related mortality. This note contributes to policy measurement by highlighting the need for routine inclusion of sibling-derived PRMR estimates in future DHS reports, alongside microdata access to support independent verification and more equitable maternal health planning.

Some Entropies Derivation for Entropy Transformed Exponential Distribution with Application to Health Data

2026-05-16T17:17:22+08:00

This study aims to estimate and comparatively evaluate the performance of four entropy measures—Havrda–Charvat, Kapur, Verma, and Mathai–Haubold—in modeling newborn weight. A quantitative approach was adopted through analytical derivations and Monte Carlo simulation techniques. The performance of each entropy measure was assessed across varying sample sizes using bias, mean squared error (MSE), and root mean squared error (RMSE) as evaluation criteria. The findings indicate that the Havrda–Charvat entropy measure demonstrates superior accuracy, consistency, and convergence toward the true entropy values, thereby exhibiting robust performance under the entropy-transformed exponential distribution (ETED). These results contribute to the theoretical development of entropy-based modeling by extending current understanding of estimator performance within ETED and providing comparative evidence on the suitability of alternative entropy measures for newborn weight modeling.

Enhancing Volatility Forecasting in the Nigerian Stock Exchange: Evaluating GARCH-Type Models and Innovation Densities

2026-05-16T17:34:07+08:00

Although volatility modeling in emerging stock markets has received increasing attention, limited research has jointly compared GARCH-type model structures under alternative symmetric and skewed innovation densities in the Nigerian capital market. This study aims to evaluate the forecasting performance of selected GARCH-type models under alternative innovation densities using daily returns of the Nigerian Stock Exchange All Share Index (NSE-ASI) from February 2012 to July 2023. A quantitative econometric time-series design was employed, involving 2,820 daily observations selected through purposive sampling based on data availability. Data were obtained from the official market database and analyzed using Maximum Likelihood Estimation, model selection criteria comprising Log-Likelihood (LL), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), and forecast accuracy measures including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). The findings indicate that the APARCH(1,1)-GED model provides the best in-sample fit, whereas the APARCH(1,1)-SGED specification produces the most accurate out-of-sample forecasts. These results demonstrate the importance of innovation density selection in capturing asymmetry and fat-tailed behavior in stock return volatility. The study concludes that incorporating skewed heavy-tailed distributions enhances volatility forecasting accuracy in the Nigerian capital market. The findings contribute to the theoretical development of conditional heteroskedasticity modeling and offer practical implications for risk management, portfolio analysis, and regulatory forecasting in emerging markets. Future research may extend this work by examining advanced nonlinear and regime-switching volatility models across broader emerging market contexts.

Robust Integral Transform Methods for the Solution of Nonlinear Fractional Ordinary Differential Equations in Viscoelastic and Biological Systems

2026-05-28T15:42:31+08:00

Nonlinear and fractional-order differential equations frequently arise in viscoelastic and biological systems; however, their solution remains challenging due to the presence of nonlocal operators, memory effects, and complex boundary conditions. Classical integral transforms, including the Laplace and Fourier transforms, often have limitations in addressing these features effectively. This study presents a robust hybrid methodology that combines the Mahgoub Transform with the Variational Iteration Method (VIM) to solve nonlinear and fractional-order ordinary differential equations (ODEs). The proposed approach was systematically applied to linear, nonlinear, and fractional-order ODEs to evaluate its convergence, accuracy, and capacity to handle memory-dependent effects. The findings demonstrate that the Mahgoub–VIM method achieves rapid convergence, high accuracy, and improved performance compared with traditional transforms such as the Sumudu Transform. These results indicate that the proposed method provides a reliable and efficient analytical framework for modeling complex viscoelastic and biological phenomena governed by nonlinear and fractional-order dynamics. This study contributes to the advancement of integral transform-based solution methods and offers practical implications for the mathematical modeling of systems characterized by memory-dependent behavior and nonlinear responses.

Effect of Credit Management on the Financial Performance of Deposit Money Banks in Nigeria

2026-05-28T15:59:52+08:00

This study investigated the effect of credit management on the financial performance of deposit money banks in Nigeria over a 25-year period from 2000 to 2024. Credit management was proxied by the non-performing loan ratio, loan-to-deposit ratio, and capital adequacy ratio, while bank performance was measured using return on equity (ROE). The study used secondary data and employed the Johansen cointegration technique to examine the existence of a long-run relationship among the variables. The results indicate the presence of one cointegrating equation at the 5% significance level, confirming a long-run equilibrium relationship. An error correction model (ECM) was subsequently estimated to capture short-run dynamics and long-run adjustment. The ECM results reveal a statistically significant and correctly signed error correction term, indicating that approximately 1.13% of short-run disequilibrium is corrected annually. Furthermore, the findings show that credit risk management variables exert negative but statistically insignificant effects on ROE. Despite the individual insignificance of the explanatory variables, the overall model is statistically significant and free from serial autocorrelation. The study concludes that credit management indicators exert a weak influence on the profitability of deposit money banks in Nigeria. These findings contribute to banking and financial performance literature by providing empirical evidence on the limited explanatory role of selected credit management indicators in determining profitability and offer practical implications for bank managers and regulators in strengthening credit risk assessment, loan portfolio quality, and capital management practices.

Analysis of the Hydromagnetic Free Convective System in the Presence of Suction/Injection

2026-05-28T16:13:09+08:00

This study examines the dynamics of fluid flow and heat transfer under impulsive and accelerated motion conditions in non-steady free convective flow systems. It aims to derive and analyze velocity and temperature profiles under the influence of key physical parameters, including the suction/injection parameter, Grashof number, and Prandtl number. A hybrid analytical–numerical method was employed, integrating Laplace transform-based analytical procedures with numerical evaluation techniques. Two cases of non-steady free convective flow, namely impulsive motion and accelerated motion, were considered. Talbot’s method for the inverse Laplace transform was applied in the accelerated motion case to further evaluate the temperature and velocity profiles. The findings show that the suction/injection parameter, Grashof number, and Prandtl number substantially influence both the velocity field and thermal field, thereby shaping the behavior of fluid flow and heat transfer under non-steady convective conditions. This study concludes that the hybrid analytical–numerical approach provides an effective framework for examining transient convective flow problems involving impulsive and accelerated motions. The findings contribute to the literature on fluid mechanics and heat transfer by offering analytical and computational insights relevant to engineering and thermal science applications.

Non-Sinusoidal Predictive Model of Premium Motor Spirit (PMS) in Nigerian Fuel Price Hike

2026-05-28T16:26:33+08:00

This study investigates the dynamics of Premium Motor Spirit (PMS) prices in Nigeria using a non-sinusoidal high-order mathematical model applied to annual data spanning 1990–2022. The proposed modelling framework is designed to represent long-term price growth behaviour and structural progression rather than periodic or cyclical movements. Model parameters were estimated using the least squares estimation technique to ensure optimal fitting of the observed price series. The adequacy of the model was evaluated through validation error metrics and correlation analysis, providing quantitative measures of goodness-of-fit and predictive reliability. The findings indicate that the non-sinusoidal high-order model effectively represents the sustained upward trajectory of PMS prices over the study period, reflecting gradual economic adjustments, inflationary pressures, and long-term policy influences. However, deviations between observed and model-generated prices were evident during periods characterized by abrupt policy interventions, subsidy reforms, and regulatory shocks, which introduced short-term irregularities into the price structure. Despite these disturbances, the model maintained a strong capacity to describe the overall price evolution and underlying trend of PMS pricing in Nigeria. This study contributes to energy price modelling literature by demonstrating the relevance of non-sinusoidal growth-based approaches for analysing long-term energy price behaviour in regulated and policy-sensitive economic environments.

Statistical Time Series Analysis on Malaria Cases among Children (0-5 Years) in Damaturu Town (A Case Study of Primary Health Care Centers, Damaturu, Yobe State, Nigeria)

2026-05-29T09:33:30+08:00

This study applied statistical time series analysis to examine malaria cases among children aged 0–5 years in Primary Health Care (PHC) centers in Damaturu, Yobe State, using monthly data from 2017 to 2024. The study aimed to describe malaria patterns, examine long-term trends, identify seasonal components, fit an appropriate Seasonal Autoregressive Integrated Moving Average (SARIMA) model, and forecast future malaria incidence. Descriptive analysis showed a sharp increase in cases from 3,503 in 2017 to 25,412 in 2024, with a total of 109,101 cases recorded during the study period. Seasonal decomposition revealed consistent peaks during the rainy months of August to October, with October recording the highest transmission levels. Stationarity was confirmed using the Augmented Dickey–Fuller test (p = 0.01). Model identification based on ACF, PACF, AIC, and BIC criteria selected SARIMA(2,0,0)(0,1,1)[12] with drift as the best-fitting model. Forecasts for 2025–2026 indicated continued increases in malaria incidence, with projected peaks exceeding 3,700 and 3,900 cases, respectively. The findings confirm a significant upward trend and strong seasonal variation in malaria incidence among children under five in Damaturu. This study concludes that malaria remains a persistent and increasing public health challenge in the study area. The findings contribute to public health surveillance and epidemiological forecasting by demonstrating the value of SARIMA-based modelling for anticipating seasonal malaria burden. Practical implications include the need to strengthen seasonal interventions, improve surveillance, enhance resource allocation, and adopt predictive modelling for timely malaria control. Future research should incorporate climatic and socio-behavioral variables to improve forecast accuracy.

Time Series Analysis on Infant Mortality Rates (A Case Study of Yobe State Specialist Hospital Geidam, 2014 - 2024)

2026-05-29T17:23:36+08:00

This study examined the pattern and trend of infant mortality rates at Yobe State Specialist Hospital, Geidam, using retrospective secondary data from 2014 to 2024. The study aimed to analyze infant mortality patterns and forecast future trends using time series techniques. A quantitative retrospective design was adopted, and the data were analyzed using descriptive statistics and time series models, including moving averages and exponential smoothing, to identify trends, seasonal fluctuations, and forecast patterns within the study period. The findings revealed that infant mortality rates fluctuated across the years, showing both seasonal and irregular variations, with a slight downward trend toward the later years. The results suggest that improved maternal care, immunization programs, and increased public health awareness may have contributed to this decline. Forecast results indicate a gradual but continuous reduction in infant mortality if current health interventions are sustained and strengthened. The study concludes that time series analysis provides an effective framework for understanding the dynamics of infant mortality and supporting evidence-based policy decisions aimed at reducing infant deaths. The findings contribute to public health monitoring and forecasting by demonstrating the usefulness of time series techniques in assessing infant mortality trends. Practical implications include the need for state and local governments, through the Ministry of Health, to strengthen maternal and child health programs, with support from international organizations such as WHO and UNICEF.