Mathematical Modeling for Road Accident Analysis in Bangladesh: Nonlinear Deterministic, Exposure-Adjusted Count, and Seasonal Time-Series Approaches

Abstract

This study establishes a coherent mathematical model for the investigation of road accidents in Bangladesh by integrating nonlinear deterministic modeling, count regression with exposure, normalized fatality-rate estimation and seasonal time-series forecasting. The analysis constructs a balanced monthly panel from January 2023 to December 2025, with 36 national monthly observations and 288 division-month observations, using four synchronized datasets on population, monthly accidents, fatalities by type of vehicle, and vehicle involvement. During the study period, Bangladesh recorded 17,046 accidents, 15,994 deaths, 20,389 injuries and 36,383 total casualties indicating a persistently high and fluctuating national toll. Analysis of the deterministic model shows that harmonic quadratic equations best describe the accidents and fatalities, a harmonic linear equation the injuries, and a cubic equation the accident severity index, confirming the absence of any single common trend structure across the burden dimensions. Seasonal-index analysis revealed that June is the month with the highest number of accidents, fatalities and injuries, while August is the lowest month for accidents and fatalities and November for injuries, indicating consistent annual patterns. At the division-month level, the negative binomial model is significantly better than the Poisson model, reducing the AIC by 275.558 points, indicating significant overdispersion in accident occurrences. The harmonic OLS model for the fatality rate accounts for 46.1% of the variation in fatalities per 100,000 individuals. The SARIMAX forecast has a 12-month seasonal memory and projects a rise in June 2026 and a fall in August 2026. The results suggest that the incidence of road accidents in Bangladesh is influenced by nonlinear trends, seasonal variations, exposure disparities, and random temporal correlations, providing a mathematically coherent basis for risk assessment and road safety strategies.