52 citations · 321 across the 18 of their papers we have counts for
12 papers · 1 filter
Entropy and the arrow of time in population dynamics
Diogo Costa-Cabanas, Fabio A. C. C. Chalub, Max O. Souza
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for…
Gradient flow formulations of discrete and continuous evolutionary models: a unifying perspective
Fabio A. C. C. Chalub, Léonard Monsaingeon, Ana Margarida Ribeiro +1
We consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenera…
Fitness potentials and qualitative properties of the Wright-Fisher dynamics
Fabio A. C. C. Chalub, Max O. Souza
We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the centr…
From fixation probabilities to d-player games: an inverse problem in evolutionary dynamics
Fabio A. C. C. Chalub, Max O. Souza
The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution.…
On the stochastic evolution of finite populations
Fabio A. C. C. Chalub, Max O. Souza
This work is a systematic study of discrete Markov chains that are used to describe the evolution of a two-types population. Motivated by results valid for the well-known Moran (M)…
On the dynamics of a class of multi-group models for vector-borne diseases
Abderrahman Iggidr, Gauthier Sallet, Max O. Souza
The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. den…
Fixation in large populations: a continuous view of a discrete problem
Fabio A. C. C. Chalub, Max O. Souza
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a…
Multiscale Analysis for a Vector-Borne Epidemic Model
Max O. Souza
Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in tw…
The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations
Fabio A. C. C. Chalub, Max O. Souza
We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types.…
The SIR epidemic model from a PDE point of view
Fabio A. C. C. Chalub, Max O. Souza
We present a derivation of the classical SIR model through a mean-field approximation from a discrete version of SIR. We then obtain a hyperbolic forward Kolmogorov equation, and s…
From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics
Fabio A. C. C. Chalub, Max O. Souza
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuou…
Global stability for a class of virus models with CTL immune response and antigenic variation
Max O. Souza, Jorge P. Zubelli
We study the global stability of a class of models for in-vivo virus dynamics, that take into account the CTL immune response and display antigenic variation. This class includes a…