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The main function of biomedical sensor network is to guarantee that the data packets from patients can be delivered reliably to the destination node or medical center. Attached to patients, these nodes can be mobile, thus forming a mobile wireless sensor network (mWSN). Moreover, non-cooperative nodes may also be present in the network. This paper therefore proposes a routing method for non-cooperative mWSNs based on Reinforcement Learning (RL). In particular, a reputation and trust scheme to avoid misbehaving nodes was integrated with an existing RL-based routing protocol called RL-QRP. We evaluated its performance in non-cooperative mWSNs under various conditions of non-cooperation and mobility. We found that the proposed method can achieve a success ratio of up to 11% over the RL-QRP, and 25% over a non-learning brute force search threshold method.