52 citations · 321 across the 18 of their papers we have counts for
21 papers
Continuous approximations for the fixation probability of the Moran processes on star graphs
Poly H. da Silva, Max O. Souza
We consider a generalized version of the birth-death (BD) and death-birth (DB) processes introduced by Kaveh, Komarova, and Kohandel (2015), in which two constant fitnesses, one fo…
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…
Identifiability and observability of the SIR model with quarantine
Frédéric Hamelin, Abderrahman Iggidr, Alain Rapaport +2
We analyze the identifiability and observability of the well-known SIR epidemic model with an additional compartment Q of the sub-population of infected individuals that are placed…
On regularized optimal execution problems and their singular limits
Max O. Souza, Yuri Thamsten
We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian sto…
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)…
A Hedged Monte Carlo Approach to Real Option Pricing
Edgardo Brigatti, Felipe Macias, Max O. Souza +1
In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from…
Conservative parabolic problems: non-degenerated theory and degenerated examples from population dynamics
Olga Danilkina, Max O. Souza, Fabio A. C. C. Chalub
We consider partial differential equations (PDE) of drift-diffusion type in the unit interval, supplemented by either two conservation laws or by a conservation law and a further b…
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…
Robustness of Cucker-Smale flocking model
Eduardo Canale, Federico Dalmao, Ernesto Mordecki +1
Consider a system of autonomous interacting agents moving in space, adjusting each own velocity as a weighted mean of the relative velocities of the other agents. In order to test…
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…
A non-standard evolution problem arising in population genetics
Fabio A. C. C. Chalub, Max O. Souza
We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck eq…
Discrete versus continuous models in evolutionary dynamics: from simple to simpler -- and even simpler -- models
Fabio A. C. C. Chalub, Max O. Souza
There are many different models--both continuous and discrete--used to describe gene mutation fixation. In particular, the Moran process, the Kimura equation and the replicator dyn…
The continuous limit of the Moran process and the diffusion of mutant genes in infinite populations
Fabio A. C. C. Chalub, Max O. Souza
We consider the so called Moran process with frequency dependent fitness given by a certain pay-off matrix. For finite populations, we show that the final state must be homogeneous…