Modeling the intermittent behavior of turbulent energy dissipation processes in both space and time is often a relevant problem when dealing with phenomena occurring in high-Reynolds-number flows, especially in astrophysical and space fluids. In this paper, a dynamical model is proposed to describe the intermittency of the energy dissipation rate in a turbulent system. This is done by using a shell model to simulate the time evolution of the turbulent cascade and introducing some heuristic rules, partly inspired by the well-known p model, to construct a spatial structure of the energy dissipation rate. In order to validate the model and to study its spatial intermittency properties, a series of numerical simulations have been performed. These show that the level of spatial intermittency of the system can be simply tuned by varying a single parameter of the model and that scaling laws in agreement with those obtained from experiments on fully turbulent hydrodynamic flows can be recovered. It is finally suggested that the model could represent a useful tool to simulate the intermittent structure of turbulent energy dissipation in those high-Reynolds-number astrophysical fluids where impulsive energy release processes can be associated with the dynamics of the turbulent cascade.