Cooperative driving relies on communication among vehicles to create situational awareness. One application of cooperative driving is Cooperative Adaptive Cruise Control (CACC) that aims at enhancing highway transportation safety and capacity. Model-based communication (MBC) is a new paradigm with a flexible content structure for broadcasting joint vehicle-driver predictive behavioral models. The vehicle's complex dynamics and diverse driving behaviors add complexity to the modeling process. Gaussian process (GP) is a fully data-driven and non-parametric Bayesian modeling approach which can be used as a modeling component of MBC. The knowledge about the uncertainty is propagated through predictions by generating local GPs for vehicles and broadcasting their hyper-parameters as a model to the neighboring vehicles. In this research study, GP is used to model each vehicle's speed trajectory, which allows vehicles to access the future behavior of their preceding vehicle during communication loss and/or low-rate communication. Besides, to overcome the safety issues in a vehicle platoon, two operating modes for each vehicle are considered; free following and emergency braking. This paper presents a discrete hybrid stochastic model predictive control, which incorporates system modes as well as uncertainties captured by GP models. The proposed control design approach finds the optimal vehicle speed trajectory with the goal of achieving a safe and efficient platoon of vehicles with small inter-vehicle gap while reducing the reliance of the vehicles on a frequent communication. Simulation studies demonstrate the efficacy of the proposed controller considering the aforementioned communication paradigm with low-rate intermittent communication.