Showing papers by "Andrea De Gaetano published in 2023"

HAPC Model of Crowd Behavior during Crises

Abstract: The dynamics of pedestrian crowds during exceptional tragic events are very complex depending on a series of human behaviors resulting from combinations of basic interaction principles and self-organization. The Alert–Panic–Control (APC) model is one of the mathematical models in the literature for representing such complicated processes, mainly focusing on psychologists’ points of view (i.e., emotion contagion). This work proposes a Hybrid APC (HAPC) model including new processes, such as the effect of resonance, the victims caused by people in state of panic, new interactions between populations based on imitation and emotional contagion phenomena and the ability to simulate multiple disaster situations. Results from simulated scenarios showed that in the first 5 min 54.45% of population move towards a state of alert, 13.82% enter the control state and 31.73% pass to the state of panic, highlighting that individuals respond to a terrible incident very quickly, right away after it occurs.

Modeling outcome trajectories in patients with acquired brain injury using a non-linear dynamic evolution approach.

Abstract: This study describes a dynamic non-linear mathematical approach for modeling the course of disease in acquired brain injury (ABI) patients. Data from a multicentric study were used to evaluate the reliability of the Michaelis-Menten (MM) model applied to well-known clinical variables that assess the outcome of ABI patients. The sample consisted of 156 ABI patients admitted to eight neurorehabilitation subacute units and evaluated at baseline (T0), 4 months after the event (T1) and at discharge (T2). The MM model was used to characterize the trend of the first Principal Component Analysis (PCA) dimension (represented by the variables: feeding modality, RLAS, ERBI-A, Tracheostomy, CRS-r and ERBI-B) in order to predict the most plausible outcome, in terms of positive or negative Glasgow outcome score (GOS) at discharge. Exploring the evolution of the PCA dimension 1 over time, after day 86 the MM model better differentiated between the time course for individuals with a positive and negative GOS (accuracy: 85%; sensitivity: 90.6%; specificity: 62.5%). The non-linear dynamic mathematical model can be used to provide more comprehensive trajectories of the clinical evolution of ABI patients during the rehabilitation period. Our model can be used to address patients for interventions designed for a specific outcome trajectory.

A System of Random ODEs for Representing Trends of CGM Signals

Abstract: Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose Monitoring) devices from six subjects with type 2 diabetes in good metabolic control at the University Polyclinic Agostino Gemelli, Catholic University of the Sacred Heart, is carried out. In particular, a system of random ordinary differential equations whose state variables are affected by a sequence of stochastic perturbations is proposed and used to extract more informative inferences from the patients' data. For this work, Matlab and R programs were used to find the most appropriate values of parameters (according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)) in models for each patient. Specifically, the fitting was carried out by using the Particle Swarm Optimization Method to minimize the ordinary least squares error between the observed CGM data and the data from the random ODE model. Goodness of fit tests were made in order to assess whether or not the exponential distribution, whose parameter had been estimated by Maximum Likelihood Estimation, was suitable for representing the waiting times computed from the model parameters. Finally, both parametric and non-parametric density estimation of the frequency histograms associated with the variability of the glucose elimination rate from blood into the external environment were conducted and their representative parameters assessed from the data. The results show that the chosen models succeed in capturing most of the glucose fluctuations for almost every patient.