Implementation and validation of a new method to model voluntary departures from emergency departments. Running Title: Modeling Voluntary departures from emergency departments.

In the literature, several organizational solutions have been proposed for determining the probability of voluntary patient discharge from the emergency department. Here, the issue of self-discharge is analyzed by Markov theory-based modeling, an innovative approach diffusely applied in the healthcare field in recent years. The aim of this work is to propose a new method for calculating the rate of voluntary discharge by defining a generic model to describe the process of first aid using a "behavioral" Markov chain model, a new approach that takes into account the satisfaction of the patient. The proposed model is then implemented in MATLAB and validated with a real case study from the hospital "A. Cardarelli" of Naples. It is found that most of the risk of self-discharge occurs during the wait time before the patient is seen and during the wait time for the final report; usually, once the analysis is requested, the patient, although not very satisfied, is willing to wait longer for the results. The model allows the description of the first aid process from the perspective of the patient. The presented model is generic and can be adapted to each hospital facility by changing only the transition probabilities between states.