On the Dynamic Interplay between Positive and Negative Affects

TL;DR

This paper presents a mathematical model of the dynamic interaction between positive and negative affects, analyzing how external events and internal states influence emotional balance and therapy outcomes.

Contribution

It introduces a delay differential equation model to study affect dynamics and compares it with psychological data, providing insights into therapy effects and emotional resilience.

Findings

Model predicts stabilization depends on historical emotional states.

Therapy impacts affect balance differently in the model.

Model aligns with data from a depressed patient.

Abstract

Emotional disorders and psychological flourishing are the result of complex interactions between positive and negative affects that depend on external events and the subject's internal representations. Based on psychological data, we mathematically model the dynamical balance between positive and negative affects as a function of the response to external positive and negative events. This modeling allows the investigation of the relative impact of two leading forms of therapy on affect balance. The model uses a delay differential equation to analytically study the complete bifurcation diagram of the system. We compare the results of the model to psychological data on a single, recurrently depressed patient that was administered the two types of therapies considered (viz., coping-focused vs. affect-focused). The model leads to the prediction that stabilization at a normal state may rely on evaluating one's emotional state through an historical ongoing emotional state rather than in a narrow present window. The simple mathematical model proposed here offers a theoretically grounded quantitative framework for investigating the temporal process of change and parameters of resilience to relapse.