A Dual Referral Healthcare Model Based On Two-tied Queueing System

The epidemic caused by 2019-n Co V hits the world in 2020.The sheer number of patients and the limited medical resources available will be a major challenge.This paper examines a community of healthcare consisting of a primary care provider and a superior hospital from the perspective of minimizing the total cost of the two-tiered service system.The design of optimal referral thresholds was studied from the point of view of the total operating costs of the system,in conjunction with the two-way referral policy,and the optimal staffing level of healthcare professionals maximizes the service capacity of the entire healthcare system and helps patients make better medical choices.We incorporate the gatekeeper theory,extending it from a one-direction referral problem to a dual referral problem,while designing different upward and downward referral threshold and promoting the original one-dimensional problem to two dimensions.On this basis,this paper builds a two-way referral model for the medical system,abstracts the patient's condition,and designs various different types of the service time of different patients and their referral needs.This paper focuses on three scenarios of healthcare system models,the first two models apply the square-root staffing rule,the difference between them lies in service rate.The first model is designed to have a fixed service rate,while the second model's service rate varies with the complexity of the condition and is also affected by other parameters.In the third model,we will relax the requirement of the number of staffing and include the number of healthcare workers as a variable to portray a more general case.In the first model,it is concluded that the objective function is generally not globally convex,and the numerical experiments show that the optimal referral threshold will be taken at the border under the parameter settings.In the second model we derive the model convexity conditions in the case of service rate variation and calculate the optimal referral threshold.In numerical experiments,we use survival curves in survival analysis and try various common expressions for time of service,draw the corresponding function images and make the analysis of optimal referral thresholds for various scenarios.In the third model,we eliminate the square-root staffing requirement and replace it with a general staffing condition,creating a mixed integer non-linear problem.To solve this problem,we use the branch & bound method to analyze the variation of the optimal referral threshold and staffing level with each parameter case.The experimental results show that applying the square-root staffing rule to the two-way referral problem for approximate optimal staffing and optimal total cost is accurate.Combining the two-way referral model for the three scenarios,this paper is able to provide a certain amount of guidance and give an accurate estimate of how the parent hospital and the primary care provider can optimize their own operations in order to achieve a win-win cooperation between the two sides.