Symmetries express the invariance of a system towards sets of mathematical transformations. In more practical terms, symmetries greatly reduce or simplify the computational efforts required to evaluate relevant properties of a system. In this paper, two methods are proposed to implement spin symmetries which simplify the analysis of the spreading of diseases in an agent-based epidemic model. We perform a set of simulations to measure the efficiency gains compared to traditional methods. Our findings show symmetry-based algorithms improve the performance of the Monte Carlo simulation and the exact Markov process.