A fractional-order spatial-temporal model for the adoption dynamics of remote healthcare services

Abstract

This paper presents a fractional-order (FO) spatial-temporal model for the adoption dynamics of Remote Healthcare Services (RHS) in a two-dimensional domain. The model incorporates memory effects and non-local temporal interactions through the Caputo nabla fractional derivative (CNFD), providing a realistic framework for social contagion processes where past states influence current behavior. The spatial domain is discretized using the Method of Lines (MOL) with periodic boundary conditions, transforming the original partial differential equations (PDEs) into a system of fractional ordinary differential equations (ODEs). We derive the equilibrium points (EPs) of the system and establish sufficient conditions for global asymptotic stability (GAS) via a Lyapunov functional (LF) approach. Numerical simulations validate the theoretical stability results, demonstrating convergence to the trivial equilibrium under the chosen parameter set. The proposed model offers a robust framework for analyzing spatial-temporal adoption dynamics with potential applications in public health, technology diffusion, and social behavior modeling.