Javier Jarillo Díaz, Universidad Complutense de Madrid.
Título: "Spatial population synchrony in two-species stochastic dynamics models".
Fecha: 26 de septiembre de 2023.
Tomás Prieto Rumeau, Universidad Nacional de Educación a Distancia.
Título: "Dispersión óptima de poblaciones: un enfoque con procesos de decisión markovianos".
Fecha: 28 de noviembre de 2023.
Josu Doncel Vicente, Universidad del País Vasco.
Título: "Performance paradox in stochastic dynamic matching models".
Fecha: 19 de diciembre de 2023.
Actividades gratuitas, pero con registro obligatorio a través de https://forms.gle/vm3Q5yfv9BhZJm5z9.
Las actividades tendrán lugar en la Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid.
Correo de contacto con los organizadores: agcorral@ucm.es.
Seminarios de investigación:
Fabio Chalub, Universidade NOVA de Lisboa.
Título: Epidemiological models and human behavior: using game theory to model the effects of voluntary vaccination.
Fecha: 17 de octubre de 2023.
Hora: 12:00 & 16:00 horas.
Lugar: Seminario Sixto Ríos.
Resumen: There are many different ways to model the spread of a disease in a population, as, for example, ordinary differential equations (deterministic models in homogeneous populations), partial differential equations (populations with space or age structure, for example), Markov process (to include stochasticity, which is important when modeling the dynamics in small populations).
One particularly important challenge is how to include human behavior into the model, which is traditionally made with the use of game theory.
In the first part, we will discuss the basic concepts of epidemiological models, based on ordinary differential equations, and game theory, with a particular interest in studying the effects of voluntary vaccinations on disease dynamics.
In the second part, we will discuss how to model the same problem using the Markov process, discuss the similarities and the differences between both models and present some challenges that can be of interest in the near future.
Miguel González Velasco, Universidad de Extremadura.
Título: Branching processes in the Markovian framework.
Fecha: 18 de octubre de 2023.
Hora: 12:00 & 16:00 horas.
Lugar: Seminario Sixto Ríos.
Resumen: Branching processes are useful probabilistic models, essentially Markovian, to describe population dynamics in the broadest sense. The notion of branching has been relevant in the development of theoretical approaches to problems in fields as diverse and applied as population growth and extinction, biology, epidemiology, cell proliferation kinetics, cancer, genetics, nuclear physics and algorithm and data structures. The seminar reviews the state of the art with regarding recent advances in the theory and applications of these models.
Antonio di Crescenzo, Università degli Studi di Salerno.
Título: Birth-death processes and their applications.
Fecha: 19 de octubre de 2023.
Hora: 12:00 & 16:00 horas.
Lugar: Seminario Sixto Ríos.
Resumen: The seminar consists of two parts. In the first part, the focus is on birth-death processes, growth models and diffusion approximations. A summary is as follows:
Birth-death processes constitute the continuous-time analog of random walks and are largely adopted as a tool for stochastic modeling. Indeed, the richness of the birth and death rates allows modeling a variety of phenomena, ranging for instance from evolutionary dynamics and neuronal modeling, to queueing and reliability theory. Various methods of analysis have been developed for determining quantities of interest, such as stationary distributions and first-passage-time distributions. This first part is aimed at providing a review of some recent results on growth-evolution models characterized by time-dependent growth rates and their stochastic counterpart described by birth-death processes. The analysis focuses on generalizations of the Gompertz and logistic growth models, and related birth-death processes having linear and quadratic rates. A diffusion approximation leading to a time-inhomogeneous geometric Brownian motion is also treated. Some applications will be outlined as well.
In the second part, the interest is in birth-death processes and related diffusions on a star graph for multi-type evolution models. An abstract is as follows:
Recent advances in the theory of birth-death processes have been oriented to describe continuous-time random walks on graphs. In this second part, we aim to discuss certain generalizations involving extended birth-death processes on a star graph defined as a lattice formed by the integers of semiaxes joined at the origin. The study is oriented to: (i) the analysis of the transient and asymptotic behavior of a multispecies birth-death-immigration process and of a continuous-time multi-type Ehrenfest model; and (ii) the construction and the study of suitable diffusion approximations for the considered models, leading to two processes belonging to the class of Pearson diffusions on the spider, i.e. a domain formed by semiaxis joined at the origin. Special attention is devoted to: the diffusion approximations involving a Feller process and the Ornstein-Uhlenbeck process; the stationary distribution based on the switching rules among the semiaxis; and the goodness of the diffusion approximation.
Mesa redonda "Procesos de Markov: casos de estudio y futuras aplicaciones":
Fecha: 20 de octubre de 2023.
Hora: 12:00 horas.
Lugar: Sala de Grados.
Los ponentes confirmados son:
Jorge Mateu Mahiques, Universitat Jaume I: Epidemias y crimen.
Grant Lythe, University of Leeds: Inmunología.
Vicent Pla Boscà, Universitat Politècnica de València: Telecomunicaciones.
Inma T. Castro, Universidad de Extremadura: Procesos industriales.
Juan Eloy Ruiz Castro, Universidad de Granada: Datos clínicos y sistemas complejos en fiabilidad.
F. Javier López, Universidad de Zaragoza: Modelos de inventario.