A Spatiotemporal Dynamics and Stability Analysis of Remote Healthcare System Adoption in Remote Hill-Track Areas

The persistent challenge of healthcare accessibility in geographically isolated regions necessitates innovative approaches to healthcare delivery and adoption modeling. This study introduces a novel mathematical framework based on reaction-diffusion systems to analyze the spatiotemporal dynamics of remote healthcare system (RHS) adoption in remote hill-track areas. Moving beyond traditional static models such as structural equation modeling (SEM), we formulate adoption dynamics through a system of coupled partial differential equations that capture the complex interplay between population awareness, adopter density, and healthcare needs. The model incorporates key sociological processes, such as social contagion, external influence, and relapse, while accounting for geographical diffusion constraints. We establish rigorous conditions for both local and global asymptotic stability of the nontrivial equilibrium through linear stability analysis and Lyapunov functional methods. Comprehensive numerical simulations validate the theoretical framework, demonstrating convergence to equilibrium states and visualizing the spatiotemporal evolution of adoption patterns. This research provides policymakers with a predictive tool for optimizing intervention strategies and resource allocation, representing a significant methodological advancement in addressing healthcare disparities in challenging environments.