Developing a Topology-Informed Mathematical Framework for Urban Network Resilience in Nigerian Megacities

Urban resilience in Nigerian megacities, particularly Lagos with a population exceeding 15 million, requires a mathematically rigorous understanding of how infrastructure network topology influences the capacity of the city system to absorb, recover from, and adapt to shocks including flooding, power outages, and traffic disruptions. This dissertation develops an original topology-informed mathematical framework for quantifying, modelling, and optimising urban network resilience that integrates algebraic topology, network science, and stochastic control theory in a unified theoretical structure. The first theoretical contribution introduces a novel resilience measure based on persistent homology of the infrastructure network that captures multi-scale connectivity properties not reflected in classical graph-theoretic metrics. A second contribution proves conditions under which this topological resilience measure is monotone with respect to network expansion operations, providing theoretical guarantees for infrastructure investment prioritisation. The third contribution formulates the infrastructure recovery problem after a stochastic disruption as an optimal stopping problem and derives the optimal recovery sequencing policy using dynamic programming on the network state space. The theoretical framework is applied to integrated transport, electricity, and water supply networks in Lagos using GIS and infrastructure asset databases from LASG. Topological resilience analysis identifies the Apapa-Oshodi corridor as the most structurally critical zone, with failure generating cascading disruptions across all three infrastructure systems. Keywords: algebraic topology, network resilience, urban infrastructure, Lagos, persistent homology.