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Mathematical model of the dynamics of psychotherapy

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Date Issued:
2012
Summary:
This is a novel attempt to produce a rigorous mathematical model of a complex system. The complex system under study is the relationship between therapists and their clients. The success of psychotherapy depends on the nature of the relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. ... We describe the emotional state of both the therapist and client with coupled, first order, nonlinear ordinary differential equations (ODE's). The rate of change of the emotional state of the therapist and client is proportional to their previous state, their uninfluenced state when alone, and an influence function which depends on the state of the other person. We formulated influence functions based on the research literature on psychotherapy and the therapeutic alliance. We then determined the critical points from the intersection of the nullclines and used a numerical ODE solver (Matlab ODE113) to compute the trajectories from different initial conditions. ... The results validate this prototypical approach to psychotherapy ; we have shown that human interaction (in the context of psychotherapy) can be quantified and modeled using differential equations.
Title: Mathematical model of the dynamics of psychotherapy.
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Name(s): Norman, Michael D.
Charles E. Schmidt College of Science
Center for Complex Systems and Brain Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 2012
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: xvi, 158 p. : ill. (some col.)
Language(s): English
Summary: This is a novel attempt to produce a rigorous mathematical model of a complex system. The complex system under study is the relationship between therapists and their clients. The success of psychotherapy depends on the nature of the relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. ... We describe the emotional state of both the therapist and client with coupled, first order, nonlinear ordinary differential equations (ODE's). The rate of change of the emotional state of the therapist and client is proportional to their previous state, their uninfluenced state when alone, and an influence function which depends on the state of the other person. We formulated influence functions based on the research literature on psychotherapy and the therapeutic alliance. We then determined the critical points from the intersection of the nullclines and used a numerical ODE solver (Matlab ODE113) to compute the trajectories from different initial conditions. ... The results validate this prototypical approach to psychotherapy ; we have shown that human interaction (in the context of psychotherapy) can be quantified and modeled using differential equations.
Identifier: 830845938 (oclc), 3358758 (digitool), FADT3358758 (IID), fau:4043 (fedora)
Note(s): by Michael Douglas Norman.
Vita.
Thesis (Ph.D.)--Florida Atlantic University, 2012.
Includes bibliography.
Mode of access: World Wide Web.
System requirements: Adobe Reader.
Subject(s): Psychotherapist and patient -- Mathematical models
Counselor and client -- Mathematical models
Therapeutic alliance -- Mathematical models
Psychotherapy -- Philosophy -- Mathematical models
Evidence-based psychotherapy
Transference (Psychology)
Countertransference (Psychology)
Held by: FBoU FAUER
Persistent Link to This Record: http://purl.flvc.org/FAU/3358758
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU