Interpretive Modelling of the Dynamics of Psycho-Emotional States Based on the Analysis of Video Streams and Systems of Differential Equations

Abstract

The aim of this study is to develop an interpretable mathematical model that describes the dynamics of a person’s psycho-emotional state based on video surveillance data. The main contribution of the research is a paradigm shift from static recording of emotions to continuous dynamic modeling. The proposed approach allows for the internal inertia of the psyche, delay effects, and relaxation processes, which are not accessible in traditional frame-by-frame analysis. The method is based on representing psycho-emotional states as a complex system, where latent variables reflect levels of calmness C(t), stress S(t), mood M(t), and exhaustion E(t). To control activity levels-visual arousal A(t), emotional valence V(t), and physical fatigue F(t)-objective markers extracted from the video stream using artificial intelligence methods are employed. The mathematical core of the model is a system of ordinary differential equations, which ensures the transparency and interpretability of the state control process. Numerical simulation was performed over a time interval of 300.0 s with a discretization step of 0.1 s. using the Runge-Kutta integration method. The maximum excitation was Amax = 0.944 at t = 145.6 s, and the stress reached a maximum of Smax = 1.0 at t = 133.5 s. To assess the model’s adequacy, we employed phase analysis methods and calculated Spearman’s rank correlation between the input features and the system’s latent states. The main results demonstrate that the proposed model effectively reproduces complex psychological effects, such as hysteresis and emotional memory. The findings are critical for the development of proactive monitoring systems in the fields of public safety and digital healthcare. The model has been validated with real-world data and allows not only for the detection of current stress but also for the prediction of recovery dynamics, thereby facilitating the timely prevention of dangerous situations from escalating.