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Threshold control policy for patient referral under cooperation scenarios

This paper addresses the issue of implementary difficulties in reverse referral that is aimed to alleviate the imbalanced utilization of Chinese tiered healthcare system. We develop a Two-level Cooperative Hospital System (TCHS) and propose a threshold control policy to analyze three scenarios of the system. In the first scenario, we determine the optimal control policy of ULH assuming all patients transferred can be accepted by some LLH. In the second scenario, we derive the optimal control policy of LLH given that the parameters such as rate of referrals will be provided by the cooperated ULH. The first two scenarios can be modeled as block-structured Markov chain and effectively solved by the method of RG-factorization. In the third scenario, we consider a referral partnership containing one ULH and one LLH. An iterative simulation approach is applied to find a tradeoff between the ULH and LLH when iteratively determining their own threshold control policies. Finally, numerical studies are carried out to validate the proposed methods. With our investigation, we provide implementable decision tools for hospitals' referral decisions.