Plasma-assisted combustion (PAC) is a promising technology that could lead to a breakthrough in propulsion systems. Many plasmas can be used for such applications. Among them, DC electric arcs are interesting because they can produce large volumes of thermal plasmas with controlled energy deposition. When such discharges are applied in a gas flow, convection entrains the head of the arc downstream while its feet remain attached to the electrodes, thus increasing the length of the arc over time. However, this growth is limited by a restrike phenomenon, which starts from streamers appearing in high electric field regions and shortcutting the long, stretched electric arc. From a numerical point of view, DC arcs can be efficiently simulated with a resistive magneto-hydrodynamics (MHD) model, with numerical requirements in terms of spatial and temporal discretization that are compatible with classic CFD and combustion simulations. However, arc restrikes rely on the propagation of streamer discharges that are highly non-neutral phenomena, whereas classical MHD assumes neutrality. To tackle this problem, we propose in this paper a model of restrike that can be used in an MHD approach. The model is based on the current knowledge about the physics of streamer discharges. After the description of the core ideas of the model, we perform a parametric study of the input parameters to examine the influence in the discharge dynamics.