A mathematical model of goal-oriented psychotherapy dynamics

Liebovitch et al. (2011) used a physical science paradigm to propose a mathematical modeling framework for the dynamics of psychotherapy. The underlying idea is that the dynamics of the psychotherapy is the result of the dyadic therapist-client interactions. This work abounds in this approach by proposing a model where the task of the therapy is to reach a prescribed goal via a feedback-based intervention of the therapist. Here, the intervention focuses on counteracting the own resistance and the client's resistance to induce a more desirable emotional valence in the client. Required conditions for the existence and stability of equilibrium points are provided, which are central to the success of the therapy process. Numerical simulations were used to illustrate the predictions of the proposed mathematical model and to gain insights into possible scenarios determining the viability of psychotherapies. In the line of the work by Liebovitch and collaborators, the main task of our work is to develop mathematical models capturing the more essential features of the therapist-client interaction with the ultimate intention of gaining insights into the complexity of psychotherapies and using the models to better train therapists.