44 citations · 216 across the 20 of their papers we have counts for
23 papers
Dynamical compatibility for finite and infinite population models used in genetics
Fabio A. C. C. Chalub, Max O. Souza
Finite and infinite population models are frequently used in population dynamics. However, their interrelationship is rarely discussed. In this work, we examine the limits of large…
Kinetic formulation of compartmental epidemic models
Carolina Strecht-Fernandes, Fabio A. C. C. Chalub
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs w…
Group centrality in optimal and suboptimal vaccination for epidemic models in contact networks
J. Orestes Cerdeira, Fabio A. C. C. Chalub, Matheus Hansen
The pursuit of strategies that minimize the number of individuals needing vaccination to control an outbreak is a well-established area of study in mathematical epidemiology. Howev…
Insuperable strategies in two-player and reducible multi-player games
Fabio A. C. C. Chalub, Max O. Souza
Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population fr…
Population dynamics and games of variable size
Matheus Hansen, Fabio A. C. C. Chalub
This work introduces the concept of Variable Size Game Theory (VSGT), in which the number of players in a game is a strategic decision made by the players themselves. We start by d…
Social \textit{vs.} individual age-dependent costs of imperfect vaccination
Fabio A. C. C. Chalub, Paulo Doutor, Paula Patrício +1
In diseases with long-term immunity, vaccination is known to increase the average age at infection as a result of the decrease in the pathogen circulation. This implies that a vacc…
A Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals
Fabio A. C. C. Chalub, Antonio Gómez-Corral, Martín López-García +1
Ordinary differential equation (ODE) models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital this is a…
Solution of the Neutral Kimura equation with two integral constraints
Fabio A. C. C. Chalub
The Kimura equation is a degenerated partial differential equation of drift-diffusion type used in population genetics. Its solution is required to satisfy not only the equation bu…
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.…
Migrations, vaccinations and epidemic control
Fabio A. C. C. Chalub, Tiago J. Costa, Paula Patrício
We consider three regions with different public health conditions. In the absence of migration among these regions, the first two have good health conditions and the disease free s…
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)…
Optimal Vaccination Strategies and Rational Behaviour in Seasonal Epidemics
Paulo Doutor, Paula Rodrigues, Maria do Céu Soares +1
We consider a SIR model with temporary immunity and time dependent transmission rate. We assume time dependent vaccination which confers the same immunity as natural infection. We…
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…
Asymptotic expression for the fixation probability of a mutant in star graphs
Fabio A. C. C. Chalub
We consider the Moran process in a graph called the "star" and obtain the asymptotic expression for the fixation probability of a single mutant when the size of the graph is large.…
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…
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…