Global stability in a networked SIR epidemic model

Abstract A graph Laplacian reaction–diffusion system is introduced to a networked SIR epidemic model. By the means of Lyapunov function, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than 1, while the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is lower than 1. We extend the stability theory of SIR models with classical Laplacian diffusion to models with graph Laplacian.