A reaction diffusion system with time delay is proposed for virus spread on bacteria immobilized on agar-coated plate. The delay explicitly accounts for a virus latent period of fixed duration. The focus is on the speed of spread of the plaque and on the existence of traveling wave solutions of the model equations, which represent a spreading plaque. We give a rigorous proof of an upper  and a lower spreading speed associated with the system and provide a proof of the existence of traveling wave solutions. Our spreading speeds give better quantitative agreement with  experimental results than earlier, non-rigorous, results.