9:30 10:15
Coupling epidemic spreading with social dynamics.
In this talk I will present a simple Susceptible-Infected-Susceptible model coupled with a continuous opinion dynamics model. Individuals can take measures to reduce the probability of contagion, and the level of effort each agent applies can change due to social interactions. We propose simple rules to model the propagation of behaviors that modify the level of effort, and analyze their impact on the dynamics of the disease. A first approximation approximation is given by a system of two ordinary differential equations describing the dynamic of the proportion of the number of infected individuals and the mean value of the effort parameter. Next, a more detailed description can be obtained by a system of two integro-differential equations for the distribution of the level of effort in the Susceptible and Infected population.
10:15 - 11:00
Kinetic modeling of socially structured opinion dynamics with epidemic spread
The COVID-19 pandemic highlighted how individual beliefs and behaviors can significantly influence the course of an epidemic. In this paper, we propose a kinetic model that associates the spread of infectious diseases with the dynamics of opinion evolving on social networks. The model captures how information and attitudes toward protective measures change in response to social influence, particularly in environments characterized by digital platforms and varying levels of connectivity. By extending classical compartmental models to include socially structured behavior, we account for the role of influential individuals and the stratified nature of online communication. Using real social media data, we calibrate the model to explore how changes in opinion contribute to the emergence and recurrence of epidemic waves. The results provide a richer understanding of the feedback between social behavior and disease dynamics, with implications for designing more effective public health interventions.
Coffe break 11:00 - 11:30
11:30 - 12:15
Attraction by pairwise coherence explains the emergence of ideological sorting.
Political polarization has become a growing concern in democratic societies, as it drives tribal alignments and erodes civic deliberation among citizens. Given its prevalence across different countries, previous research has sought to understand under which conditions people tend to endorse extreme opinions. However, in polarized contexts, citizens not only adopt more extreme views but also become correlated across issues that are, a priori, seemingly unrelated. This phenomenon, known as “ideological sorting”, has been receiving greater attention in recent years but the micro-level mechanisms underlying its emergence remain poorly understood.
Here, we study the conditions under which a social dynamic system is expected to become ideologically sorted as a function of the mechanisms of interaction between its individuals. To this end, we developed and analyzed a multidimensional agent-based model that incorporates two mechanisms: homophily (where people tend to interact with those holding similar opinions) and pairwise-coherence favoritism (where people tend to interact with ingroups holding politically coherent opinions). We numerically integrated the model’s master equations that perfectly describe the system’s dynamics and found that ideological sorting only emerges in models that include pairwise-coherence favoritism. We then compared the model’s outcomes with empirical data from 24,035 opinions across 67 topic and found that pairwise-coherence favoritism is significantly present in datasets that measure political attitudes but absent across topics not considered related to politics. Overall, this work combines theoretical approaches from system dynamics with model-based analyses of empirical data to uncover a potential mechanism underlying the pervasiveness of ideological sorting.
12:15 13:00
History and present of the Cucker-Smale model
In this talk we will explore the model developed by Felipe Cucker and Steve Smale, which plays an important role in the study of flocking dynamics. We associate this concept with collective behavior in which a large number of animals organize themselves into a coordinated movement. We can think of a flock, a school of fish, or the grazing of ungulate mammals.
We will study the advances made in this field, from the first results in 2007 to the present. We will primarily work with the concept of asymptotic flocking: a collective behavior in which a population, without central coordination, remains together while its velocities asymptotically converge to a common one. We will examine different conditions under which the model satisfies this characteristic.
09:30 10h15
Finite time blow-up for consensus dynamics and applications
We introduce a new class of kinetic equations to explore mass-dependent effects in Fokker-Planck-type models originally developed for quantum indistinguishable particles in a spatially homogeneous setting. By analyzing the resulting PDE governing particle density evolution, we characterize the regimes in which a critical mass leads to finite-time blow-up of the solution. Finally, we discuss the implications of these findings for global optimization problems.
10:15 11:00
A multiscale framework for analyzing traffic congestion through infection spreading dynamics.
Traffic congestion is a common problem in cities all around the world. It causes losses in terms of time, money and pollution, and dampens the functionality of the transportation infrastructure, critical in the context of catastrophes such as earthquakers, wildfires and others. Planning for transportation systems which are resilient to traffic congestion is essential for cities. Modeling daily traffic patterns can help by allowing to explore the effect of actions looking to palliate its effect. However, modeling traffic can be challenging, as available models are highly complex both in terms of calibration and computation. Recently, scientists have started to consider the use of simple compartmental models like the SIR (Susceptible-Recovered-Infected) to describe daily traffic congestion in terms of spreading and recovery rates. While the resulting description provides an overall picture of the dynamics, it is extremely aggregated, disregarding differences across space completely.
Here we consider the use of spatially distributed SIR models for describing daily traffic congestion. We model traffic congestion in a region by splitting it into subregions of interest, and consider coupled spreading dynamics among them. This leads to a coupled set of differential equations that allows capturing differences across subregions. To calibrate these models we use realistic traffic conditions produced with the traffic microsimulator SUMO, and phone-based mobility information from the San Francisco Bay Area in the US. We consider multiple scales by splitting the region into different numbers of subregions in a hierarchical way (and thus subregions at finer scales are contained in subregions at coarser scales) using the uber h3 library. However, as we move into smaller subregions of the order of thirty square kilometers, the number of parameters becomes too large to allow for calibration solely based on data. Taking inspiration in the mean-field approach, we regularize the fitting at different levels by linking the spreading coefficients of a given subregion with its direct parent. The mean field approach allows obtaining analytical approximations linking the spreading and recovery rates of a region and its children subregions.
The resulting framework allows for a modeling approach that is consistent through different scales, allowing for faster calibration and reduced error. By applying the framework to traffic in San Francisco, we study which subregions affect the most the overall traffic congestion, and how they affect each other. The results move a step forward in the potential of the use of compartmental models for congestion reduction planning.
Break 11:00 - 11:30
11:30 12:15
Optimal control strategies for epidemic dynamics
This talk presents a mathematical framework that integrates the classical SIR epidemic model with the Lotka-Volterra predator-prey system to jointly capture disease dynamics and ecological interactions. The resulting SIR-Lotka-Volterra model describes the interplay between hosts, vectors, and their natural predators. This coupled system offers a versatile tool to investigate the impact of ecological interventions—such as the introduction of predators targeting disease vectors—on the control and potential suppression of infectious disease outbreaks.
12:15 13:00
Kinetic Methods for Consensus-Based Segmentation
Image Segmentation is a fundamental task in the context of image processing and computer vision that consists of partitioning an image into subsets of pixels that share similar properties so as to facilitate the analysis and interpretation of the visual data. There are a wide range of applications for this technique, particularly for the analysis of biomedical images.
In this talk I will present a new approach based on Consensus-Based Models for the Image Segmentation task [1, 3]. By considering each pixel as a particle characterize by a 2D vector position and a static feature we propose a virtual interaction scheme based on the Hegselman-Krause Model that will determine the asymptotic formation of a finite number of clusters [2]. I will discuss the application of this method to a variety of biomedical images. This work has been done with the collaboration of Fondazione Mondino.
[1] Cabini, R.F.; Figini, S.; Lascialfari, A.; Pichiecchio, A.; Zanella, M. A kinetic approach to consensus-based segmentation of biomedical images. Kinetic and Related Models, 2025, 18(2): 286-311
[2] Herty, M.;Pareschi, L.; Visconti, G. Mean field models for large data–clustering problems. Networks and Heterogeneous Media, 2020, 15(3): 463-487
[3] Cabini, R.F.; Tettamanti, H.; Zanella, M. Understanding the Impact of Evaluation Metrics in Kinetic Models for Consensus-Based Segmentation. Entropy 2025, 27, 149. https://doi.org/10.3390/e27020149