The input-to-state stability (ISS) property is combined with model predictive control (MPC) of systems with time-delays and disturbances. We derive conditions such that an MPC scheme assures ISS for a single system and each subsystem of a network. To this end, it is shown that the cost functionals of the used MPC scheme are ISS-Lyapunov-Krasovskii functionals. Recent results of the stability analysis of networks using Lyapunov-Krasovskii functionals are applied. Moreover, we show that the whole network with time-delays possesses the ISS property after application of a control obtained by an MPC scheme under a small-gain condition.