global asymptotic stability of a networked fractional sir model

In this paper, we consider a networked fractional sir model. after proving the existence and uniqueness of the solution, we obtain the basic reproduction number, the disease-free equilibrium point and the endemic equilibrium point. by constructing the lyapunov function, we show that the endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than 1, and the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1. finally, numerical simulations are carried out to verify these theoretical results. thus, the stability theory of laplacian diffusion is extended to the graph laplacian model.