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For the purpose of efficient simulations, we devise a parallel solution algorithm targeting multi-socket shared-memory architectures. The model integrates infectious dynamics as continuous-time Markov chains and available data such as animal movements or aging are incorporated as externally defined events. To bring out parallelism and accelerate the computations, we decompose the spatial domain and optimize cross-boundary communication using dependency-aware task scheduling. Using registered livestock data at a high spatiotemporal resolution, we demonstrate that our approach not only is resilient to varying model configurations but also scales on all physical cores at realistic workloads. 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