44 citations · 216 across the 20 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…