This paper introduces a kinetic model of crowd evacuation from a bounded domain, integrating social behavior and contagion dynamics. The model describes the spatial movement of individuals in a crowd, taking into account interactions with other people and the geometry of the environment. Interactions between healthy and infectious individuals can lead to disease transmission and are considered. The approach is grounded in the kinetic theory of active particles, where the activity variable represents both the infectious disease status of individuals (e.g., susceptible, infected) and the psychological state of pedestrians, including contagion awareness. Varying awareness levels influence individual behavior, leading to more cautious movement patterns, potentially reducing the overall infection rate. The performance of the model is evaluated through a series of numerical simulations. Different scenarios are examined to investigate the impact of awareness levels on pedestrian behavior, infectious disease spread, and evacuation times. Additionally, the effects of population immunization and individual contagion awareness are assessed to determine the most effective strategy for reducing infections. The results provide valuable insights into targeted strategies to mitigate contagion.

This paper introduces a kinetic model that couples social behavior in crowds (such as social interpersonal distance or herding) with contagion dynamics. The approach is based on the so-called kinetic theory of active particles where the activity variable represents the psychological state of pedestrians as well as their state related to an infectious disease (e.g., susceptible, infected, etc.). The activity evolves as the crowd moves and eventually exits a closed room. Some case studies are proposed in order to demonstrate the role of activity and how contagion awareness and stress influence the crowd movement and its shaping behavior.

Electrical impedance tomography (EIT) combined with machine learning has shown promise for the classification of strokes. However, most previous works have used raw EIT voltage data as network inputs. We build upon a recent development which suggested the use of a special noise-robust virtual hybrid edge detection (VHED) functions computed from EIT data as network inputs, although that work used only simplified and mathematically ideal models. In this work, we design models with high detail and mathematical realism. Virtual patients are created using a physically detailed 2D head model which includes features known to create challenges in real-world imaging scenarios. Simulated noisy EIT electrode data, generated using the realistic complete electrode model as opposed to the mathematically ideal continuum model, is processed to obtain VHED functions. We compare the use of VHED functions as inputs against the alternative paradigm of using raw EIT voltages. Our results show that (ⅰ) stroke classification can be performed with high accuracy using 2D EIT data from physically detailed and mathematically realistic models, and (ⅱ) in the presence of noise, VHED functions outperform raw data as network inputs.

Understanding pedestrian dynamics is critical for mitigating crowd-related risks and improving public safety. In this work, we propose a novel data-driven mesoscopic modeling framework that combines the kinetic theory of active particles (KTAPs) with data assimilation techniques, thereby offering a data-driven learning approach applicable to collective systems with learning and decision-making behavior, in line with recent KTAP developments in this area. The framework uses an ensemble Kalman filter to sequentially estimate the time-dependent spatial distribution of pedestrians and model parameters by fusing observations with the mesoscopic forward model state. Through a series of twin experiments, we show that the panic factor—a key behavioral parameter—is identifiable within this framework. We also evaluate the robustness of the approach by assimilating synthetic observations generated by an agent-based model (ABM). This setup introduces structural model error because the ABM is governed by microscopic rules that differ fundamentally from the mesoscopic kinetic equations. Despite this discrepancy, the ensemble Kalman filter, through the observation-based innovation term, successfully drives the kinetic model to track the observed pedestrian density while simultaneously recovering the panic factor. In this framework, observations act as a physical constraint on the evolution of the kinetic model. Crowd-dynamics models, including ABMs and kinetic models, often rely on phenomenological terms to describe social interactions, with parameters that are highly uncertain. Our findings indicate that in such systems, free-running simulations inevitably may diverge from the true state, whereas an online data-driven approach effectively constrains the system’s trajectory to its underlying dynamical manifold.

Diffuse optical tomography (DOT) is an imaging modality in which images of the optical properties of a biological tissue, specifically diffusion [Formula: see text] and absorption [Formula: see text], are estimated based on measurements of near-infrared light on the surface of the body. In practical applications, one often lacks exact knowledge of the measurement domain boundary. This poses a significant challenge, as inaccuracies in the boundary shape of the computational domain may result in substantial artifacts in the reconstructed images. In this study, the following two results are achieved in a two-dimensional setting: (i) when the measurement domain [Formula: see text] is known, it is shown that knowledge of the Robin-to-Neumann map for two modulation frequencies uniquely determines [Formula: see text] and [Formula: see text], both assumed to be isotropic. (ii) When the measurement domain [Formula: see text] is not exactly known, a method is proposed for simultaneous reconstruction of [Formula: see text] and [Formula: see text] as well as the boundary [Formula: see text]. For this, DOT measurements are needed for two modulation frequencies. This approach yields reconstructed coefficients that are a conformal deformation of the true coefficients in the exact domain. The new method is demonstrated using simulated noisy data.