On Nonlinear Poverty–Hunger Model for Sustainability and Basic Needs: Awareness Feedback, Threshold Dynamics, and Attention-Enhanced Reservoir Computing

Eradicating poverty and hunger (SDG 1 and SDG 2) is central to sustainable development and environmental stability. This study proposes a nonlinear dynamical model describing the coupled evolution of poverty and hunger under awareness-driven mitigation strategies. The population is divided into socio-economically secure, poor, food-insecure, and co-burdened groups, together with a dynamic awareness variable that reduces transitions into adverse states. The model incorporates bidirectional coupling, endogenous reinforcement, partial recovery, and exogenous socio-economic shocks linked to climate variability and policy disruptions. Qualitative analysis establishes positivity, boundedness, and invariant regions. A poverty–hunger reproduction number derived via the next-generation matrix determines the local stability of the poverty–hunger-free equilibrium. A high-order numerical framework combining quasilinearization with shifted Legendre spectral collocation and domain decomposition is developed to simulate the model dynamics; this approach enables spectrally accurate, stable long-horizon simulations and provides a globally smooth solution approximation that supports the subsequent data-driven forecasting stage. Attention-enhanced reservoir computing is further employed to investigate the forecasting capability of data-driven models for reproducing the temporal dynamics generated by the proposed system. The framework supports evidence-based policies toward sustainable livelihoods and basic-needs security.