The challenge of optimising traffic flow in urban areas is exacerbated by varying road conditions and unpredictable traffic patterns. A mathematical framework was established to simulate traffic scenarios. The model incorporates data from the Senegalese transportation network and uses asymptotic analysis to assess its stability under different conditions. The simulation revealed that traffic congestion is significantly influenced by road construction projects, with a reduction of 15% in congestion levels observed when these projects are completed. This study provides insights into the impact of infrastructure improvements on traffic flow efficiency. Future research should explore the economic impacts and broader implications of traffic management policies based on this model. traffic optimization, numerical simulation, asymptotic analysis, Senegal Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.