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We investigate a model of drug administration in the con- text of a plaque-formation process responsible of Alzheimer’s disease. This is a polymerisation process, best described by a rule-based model to counteract the intrinsic combinatorial explosion of the underlying re- action network. Furthermore, there is the additional complicancy of time- dependent rates, modelling the effect of drugs. In the paper, we provide a novel and efficient rejection-based simulation algorithm that samples exactly the trajectory space and apply it to study the efficacy of different drug administration policies.