DMA - Artículos

The Mathematical Theory of Behavioural Swarms: Towards Modelling the Collective Dynamics of Living Systems

2026-01-15T11:46:59Z

The Mathematical Theory of Behavioural Swarms: Towards Modelling the Collective Dynamics of Living Systems Fabregas, Rene; Liao, Jie; Outada, Nisrine Classical swarm models, exemplified by the Cucker–Smale framework, provide foundational insights into collective alignment but exhibit fundamental limitations in capturing the adaptive, heterogeneous behaviours intrinsic to living systems. This paper formalises the mathematical theory of Behavioural Swarms, a comprehensive framework where each particle’s state incorporates a dynamic internal variable, the activity that co-evolves with position and velocity through nonlocal interactions. We demonstrate how this approach transcends prior models by integrating adaptive decision-making mechanisms and heterogeneous behavioural states into rigorous differential systems. Through applications in behavioural economics and crowd dynamics, we establish the theory’s capacity to predict emergent macroscopic patterns from individual behavioural states. Our critical analysis positions this framework against kinetic theories of active particles and agent-based approaches, revealing distinct advantages for modelling systems where individual agency drives collective outcomes.

Data-driven modelling of IRCU patient flow during the COVID-19 pandemic

2026-01-15T11:41:17Z

Data-driven modelling of IRCU patient flow during the COVID-19 pandemic Navas-Ortega, Ana Carmen; Sánchez Martínez, José Antonio; García-Flores, Paula Isabel; Morales-Garcia, Concepcion; Fabregas, Rene Intermediate Respiratory Care Units (IRCUs) are vital during crises like COVID-19. This study evaluated clinical outcomes and operational dynamics of a new Spanish IRCU with specialised staffing. A prospective cohort study (April-August 2021) included 249 adult patients with COVID-19 respiratory failure (UHVN IRCU, Granada). Data on demographics, Non-Invasive Ventilation (NIV), length of stay (LOS), and outcomes (ICU transfer, exitus, recovery) were analysed. Patient flow was simulated using a data-calibrated deterministic compartmental model (Ordinary Differential Equations, ODEs) that represented state transitions, and an empirical LOS-based stochastic convolution model that incorporated admission variability. The median age was 51; 31% of patients required NIV. NIV patients were older (median 61 vs 42, p<0.001). Overall, 8% needed ICU transfer; 3% experienced in-IRCU exitus. Notably, no ICU transfers or deaths occurred among 172 non-NIV patients. Of 77 high-risk NIV patients, 68% recovered in IRCU without ICU escalation. The ODE model, based on transition rates between patient states, reflected aggregate outcomes. Both modelling approaches demonstrated system strain during admission surges (partially mitigated by simulated improvements in care efficiency via parameter modulation) and yielded consistent peak occupancy estimates. This IRCU, with specialised staffing, effectively managed severe COVID-19. High recovery rates, especially for NIV patients, potentially eased ICU pressure. Dynamic modelling confirmed surge vulnerability but highlighted the benefits of care efficiency from modulated transition parameters. Findings underscore positive outcomes in this IRCU model and support such units in pandemic response. We are truly grateful to every patient who generously dedicated their time and effort to be part of our study. We also want to convey our deep appreciation to the exceptional medical and nursing staff of the IRCU at the UHVN in Granada, Spain. Their unwavering dedication, tireless efforts, and unparalleled expertise have been instrumental in maintaining the seamless functioning of the IRCU and providing outstanding care to our patients. Their remarkable teamwork and exceptional skills have been indispensable in delivering our patients the utmost quality of care. RF acknowledges partial support from the María Zambrano-Senior grant (Spanish Ministerio de Universidades and Next-Generation EU); Grant C-EXP-265-UGR23 funded by Consejería de Universidad, Investigación & Innovación & ERDF/EU Andalusia Program; Grant PID2022-137228OB I00 funded by the Spanish Ministerio de Ciencia, Innovación y Universidades, MICIU/AEI/10.13039/501100011033 & “ERDF/EU A way of making Europe”; and the Modeling Nature Research Unit, project QUAL21-011.

On global solutions to some non-Markovian quantum kinetic models of Fokker-Planck type

2026-01-12T07:54:57Z

On global solutions to some non-Markovian quantum kinetic models of Fokker-Planck type Alejo Planas, Miguel Ángel; López Fernández, José Luis In this paper, global well-posedness of the non-Markovian Unruh-Zurek and Hu-Paz-Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of a Wigner-Poisson like equation subjected to a dissipative Fokker-Planck mechanism with time-dependent coefficients of integral type, which makes necessary to take into account the full history of the open quantum system under consideration to describe its present state. From a mathematical viewpoint this feature makes particularly elaborated the calculation of the propagators that take part of the corresponding mild formulations, as well as produces rather strong decays near the initial time (t=0) of the magnitudes involved, which would be reflected in the subsequent derivation of a priori estimates and a significant lack of Sobolev regularity when compared with their Markovian counterparts. The existence of local-in-time solutions is deduced from a Banach fixed point argument, while global solvability follows from appropriate kinetic energy estimates. Access provided by Consorcio de Bibliotecas Universitarias de Andalucía / CBUA; The first author would like to thank Departamento de Matemática Aplicada of University of Granada (Spain) and IMUS of the University of Sevilla (Spain), where part of this work was completed, for its kind hospitality and support. He was funded by Product. CNPq grant (Brazil) no. 305205/2016-1 and VI PPIT-US program ref. I3C. The second author was supported in part by MINECO (Spain), Project MTM2014-53406-R, FEDER resources, as well as by Junta de Andalucía Project P12-FQM-954. The referees are kindly acknowledged for pointing out some ideas which have contributed to improve an earlier version of this work.

Well-posedness of a Schrödinger-Poisson model describing nonlinear chiral effects

2026-01-12T07:19:58Z

Well-posedness of a Schrödinger-Poisson model describing nonlinear chiral effects López Fernández, José Luis The purpose of this paper is to investigate the well-posedness of a Schrödinger-Poisson system with additional chiral nonlinearity proportional to the electric current. More precisely, a unique mild solution of the nonlinear initial value problem associated with his model is shown to exist globally in the (weighted) energy space

Modeling chemotaxis with nonstandard production/degradation mechanisms from Doebner-Goldin theory: existence of solitary waves

2026-01-09T13:45:19Z

Modeling chemotaxis with nonstandard production/degradation mechanisms from Doebner-Goldin theory: existence of solitary waves Alejo Planas, Miguel Ángel; López Fernández, José Luis In this paper we investigate various forms of the chemical production-degradation mechanism in a chemotactic system of Keller-Segel type under which the existence of solitary wave solutions is guaranteed. Specifically, the existence of sech-type or compactly supported solitary wave solutions as well as exponential traveling wave profiles for the cell concentration is shown under certain conditions on the physical parameters