A Nonlinear Mathematical Model for AI Integration and Resource Dynamics in Healthcare

This study presents a two-dimensional nonlinear mathematical model to investigate the dynamic interaction between healthcare resources and artificial intelligence (AI) adoption in the healthcare sector. The model is inspired by classical predator–prey dynamics, where healthcare resources represent the foundational system that supports AI deployment, while AI adoption evolves through interaction with these resources and, in turn, influences their utilization. Equilibrium points of the model are derived, and their stability is analyzed using linearization techniques. The analysis reveals a trivial unstable equilibrium and a non-trivial coexistence equilibrium that exhibits neutral stability with sustained oscillatory behavior. Numerical simulations, obtained using a fourth-order Runge–Kutta method, support the analytical findings and illustrate periodic fluctuations in healthcare resources and AI adoption over time. These oscillations highlight the role of feedback mechanisms in shaping the long-term dynamics of AI integration. Although simplified, the proposed framework provides qualitative insights into the conditions required for balanced and sustainable AI adoption without compromising healthcare infrastructure. The model offers a theoretical foundation for future extensions incorporating policy interventions, resource constraints, and system heterogeneity to support informed decision-making in healthcare planning.