Document Type : Research Article
Authors
Department of Mathematics, Gauhati University, Jalukbari, Assam 781014, India
Abstract
This paper presents a deterministic nonlinear dynamical model to investigate the interactions among migration, unemployment, job availability, public resources, and environmental pollution. We establish that, under nonnegative initial data, the model solutions remain bounded, and we use analytical methods to demonstrate the existence of feasible endemic equilibria and to establish conditions for local and regional asymptotic stability. For the selected parameter set, four feasible endemic equilibria are identified, of which only one is locally asymptotically stable. To mitigate the adverse effects of unregulated migration surges, such as rapid resource depletion and severe pollution, we formulate an optimal control problem and apply Pontryagin’s Maximum Principle to design intervention strategies that reduce migration intensity and pollution levels. Numerical simulations support the theoretical conclusions and show that a combination of socioeconomic and environmental measures provides the most effective and balanced outcome. The study emphasizes the importance of coordinated policy approaches for achieving long-term regional sustainability.
Highlights
- A five-dimensional migration–environment–labour ODE model is developed.
- A unique stable endemic equilibrium is identified, and stability conditions are derived.
- Global asymptotic stability is established via a quadratic Lyapunov function.
- Optimal migration regulation and pollution controls are derived via the Pontryagin principle.
- Combined socio-economic and environmental controls outperform single-strategy interventions.
Keywords
- Human migration
- Environmental sustainability
- Unemployment dynamics
- Optimal control
- Socio-economic modeling
Main Subjects
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