Journal of Advances in Mathematics and Computer Science

The increasing dominance of motorcycles as a primary mode of transport in many urban areas across developing countries, especially in Kisii Town, Kenya, presents unique challenges to traffic modeling and management. Unlike traditional vehicular flow, motorcycle dynamics exhibit significant non-lane-based movement, high maneuverability, and interactions with multiple heterogeneous agents in a spatially constrained and disordered road network. This study develops a mathematical and computational model to capture the microscopic and macroscopic behaviors of motorcycle flow within a disordered heterogeneous traffic environment. Using continuum theory coupled with agent-based modeling, the study integrates spatial-temporal traffic variables, vehicle interaction forces, and real-time constraints reflective of Kisii’s unique road topology and rider behavior. The model incorporates stochastic elements to reflect uncertainty in rider decisions and adapts classical traffic flow theories such as LWR and Payne-Whitham frameworks to account for the mixed nature of flow. Field data from Kisii’s CBD and feeder roads are used for calibration and validation. Simulation results highlight key systemic inefficiencies, congestion hotspots, and lane-usage patterns, revealing the nonlinear dynamics of motorcycle interactions with other traffic agents. The findings provide a foundation for policy formulation, signal timing optimization, non-motorized infrastructure design, and the development of adaptive traffic control strategies specific to disordered African urban settings.