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Many important biological problems can be modeled as contagion diffusion processes over interaction networks. This paper shows how the EpiSimdemics interaction-based simulation system can be applied to the general contagion diffusion problem. Two specific problems, computational epidemiology and human immune system modeling, are given as examples. We then show how the graphics processing unit (GPU) within each compute node of a cluster can effectively be used to speedup the execution of these types of problems by an additional 3.3-fold over a CPU-only solution.