The Firefighter Problem (FP) is a graph-theoretical problem that represents the containment of diffusive processes such as fires or epidemics. This paper proposes a novel integer quadratically constrained program (IQCP) for the FP that substantially reduces the number of decision variables relative to Hartnell’s classical integer linear program (ILP). While Hartnell’s ILP has 2nT binary variables, the proposed IQCP has \(nT+n\) binary variables, where n is the order of the graph and T is an upper bound on the number of steps until the fire spreads no more. To assess the practical effectiveness of the proposed IQCP, we conduct a series of experiments using Erdős–Rényi instances spanning a range of densities, and state-of-the-art optimization solvers with default settings and a common stopping criterion (proving optimality). We also examine sensitivity to instance properties, finding conditions under which models with quadratic constraints yield shorter execution times. From these experiments, we observe that the IQCP can serve as an efficient alternative under specific conditions; specifically, when the number of fire sources and firefighters is small.