Actividades del semestre 1

Ciclo de conferencias

Semana de investigación


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.


Fabio Chalub, Universidade NOVA de Lisboa.

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.

Antonio di Crescenzo, Università degli Studi di Salerno.

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. 


Fecha: 20 de octubre de 2023.

Hora: 12:00 horas.

Lugar: Sala de Grados.

Los ponentes confirmados son: