A new fractional-order anomalous epidemic model on complex networks based on continuous-time random walk and its...

A novel fractional-order susceptible-infected-susceptible (SIS) epidemic model incorporating anomalous diffusion in heterogeneous networks is proposed, derived from the continuous-time random walk (CTRW) framework, to capture the significant effects of individual residence times and network topology on epidemic spreading. We begin by deriving the fractional-order reaction-diffusion model on complex networks from the CTRW framework. The existence and uniqueness of solutions on [0,∞), as well as those of the disease-free and endemic equilibria, are then established. Subsequently, we analyze the global asymptotic stability of the disease-free equilibrium when R0<1 and the local asymptotic stability of the endemic equilibrium when R0>1. Finally, the Ulam-Hyers stability of the SIS epidemic model is investigated. Theoretical analysis and numerical simulations demonstrate that the memory effects induced by power-law waiting times influence the convergence rate of the solution toward the steady state. When R0>1, the density of infected individuals converges to 1-1R0. Moreover, the steady-state number of infected individuals on each network node is approximately linearly related to the degree of node, and the number of individuals on each node converges to a constant multiple of the eigenvector component corresponding to the 0 eigenvalue of matrix A, clearly reflecting the effect of network topology on disease transmission.