Mathematical Modelling of Urban and Smart Cities

Rapid urban growth places pressure on resources, infrastructure, housing, and public services, creating challenges for sustainable development and urban governance. This study extends a classical urban dynamics model by incorporating smart city resource allocation and examines the contribution of mathematical modeling to urban planning and management. The model includes time-dependent smart city resource allocation, S(t), resource availability, R, the resource replenishment rate, α, and the resource depletion rate, β. These components provide a framework for examining relationships among urban growth, resource availability, and allocation decisions. A mathematical modeling and simulation approach was employed, with the model implemented and explored through numerical simulations in MATLAB. Lagos served as the case-study context for interpreting the implications of urban expansion and resource management. The analysis considered the potential role of mathematical models in anticipating urban growth, assessing sustainability challenges, and informing governance decisions. The findings suggest that uncontrolled urban expansion can contribute to resource depletion and associated social challenges. They highlight the importance of aligning resource allocation with population-related demands and the capacity to replenish available resources. The study recommends that government authorities pursue coordinated smart city initiatives addressing infrastructure development, housing provision, public service delivery, and decentralization to support urban stability. Mathematical modeling can assist these efforts by making assumptions about growth and resource dynamics explicit and providing a structured basis for examining planning options. The study concludes that integrating resource considerations into urban dynamics models offers a useful framework for investigating sustainable city development. Further empirical calibration and validation would strengthen confidence in the model’s predictive performance and clarify its applicability to Lagos and other urban contexts.