Stochastic Optimal Control Framework for Climate-Induced Migration: Age-Structured Population Dynamics in Nigeria's Coastal Regions
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249-274
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10.58578/ajstea.v4i3.8920
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Authors:Samuel O. Adeyemo1*, Amarachukwu I. O. Ofomata2, Prisca Duruojinkeya3
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Abstract
This paper develops a stochastic optimal control framework for modeling age-structured population dynamics under climate-induced migration, with application to Nigeria’s Niger Delta region. Climate-related slow-onset and extreme hazards, including flooding, sea-level rise, and environmental degradation, drive internal displacement that disproportionately affects younger working-age groups and intensifies urban demographic pressure and infrastructure strain. The proposed model extends the deterministic McKendrick–von Foerster equation into a stochastic partial integro-differential system by incorporating a climate-sensitive migration kernel with multiplicative Wiener noise to represent persistent uncertainty and optional Lévy jumps to capture abrupt extreme events. Policy interventions, including relocation incentives, infrastructure capacity enhancements, and adaptive zoning, are formulated as controls to minimize an expected long-term cost functional that penalizes demographic imbalances, intervention effort, and migration-related disruptions. Optimality conditions are derived from an adapted stochastic Pontryagin maximum principle in infinite-dimensional spaces, resulting in a forward–backward stochastic partial differential equation system. The well-posedness of the state dynamics is proven using semigroup theory and fixed-point methods, the existence of optimal controls is established through compactness and continuity arguments, and long-term ergodic behavior under persistent noise is analyzed using Lyapunov functionals. Numerical solutions combine finite-difference discretization of the age variable, Euler–Maruyama time-stepping, and Monte Carlo integration for stochastic terms, with convergence demonstrated under Lipschitz and stability assumptions. A case study in Rivers State, centered on Port Harcourt and involving an estimated population of approximately 7 million, is calibrated using UN World Population Prospects age distributions, World Bank Groundswell Africa internal climate migration projections, and regional flood probability estimates. Simulations indicate that stochastic optimal policies reduce expected urban demographic overload variance by 20–35% relative to deterministic baselines under representative flood scenarios, while promoting more balanced age structures and supporting resilient urban planning. The study contributes to environmetrics by advancing uncertainty quantification for climate-induced migration modeling and provides a reproducible Python-based decision-support framework for evidence-based policy in climate-vulnerable coastal developing regions.
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