An integer programming model to assign patients based on mental health impact for tele-psychotherapy intervention during the Covid–19 emergency

The Covid–19 pandemic challenges healthcare systems worldwide while severely impacting mental health. As a result, the rising demand for psychological assistance during crisis times requires early and effective intervention. This contributes to the well-being of the public and front-line workers and prevents mental health disorders. Many countries are offering diverse and accessible services of tele-psychological intervention; Ecuador is not the exception. The present study combines statistical analyses and discrete optimization techniques to solve the problem of assigning patients to therapists for crisis intervention with a single tele-psychotherapy session. The statistical analyses showed that professionals and healthcare workers in contact with Covid–19 patients or with a confirmed diagnosis had a significant relationship with suicide risk, sadness, experiential avoidance, and perception of severity. Moreover, some Covid–19-related variables were found to be predictors of sadness and suicide risk as unveiled via path analysis. This allowed categorizing patients according to their screening and grouping therapists according to their qualifications. With this stratification, a multi-periodic optimization model and a heuristic are proposed to find an adequate assignment of patients to therapists over time. The integer programming model was validated with real-world data, and its results were applied in a volunteer program in Ecuador.