Abstract
We obtain L-infinity-Bounds for the solution of a system of time space fractional reaction-diffusion equations modeling the geographical spread of an infectious disease or a rumor or an information within a large but finite population. The analysis is based on the application of the maximum principle to a judicious Lyapunov function. The large time behavior of the solution of the system is also discussed. (C) 2019 Elsevier Ltd. All rights reserved.