arXiv subjects

Antoine Perasso

Publications and source records attributed to Antoine Perasso.

7 recordsLinked to original sources

arXiv2026

Global stability in an age-structured SIRS malaria transmission model

This paper proposes and analyzes a malaria transmission model structured by the chronological age of the human host population. The model couples an age-structured SIRS system for humans, incorporating waning immunity, with an SI system for mosquitoes under mass-action transmissions. Using integrated semigroup theory and spectral analysis, we establish the well-posedness of the model, derive the basic reproduction number, and prove the global asymptotic stability of the parasite-free equilibrium by using a Lyapunov functional, when $R_0\leq 1$, thereby excluding the possibility of backward bifurcation. Numerical simulations further suggest the global stability of the endemic equilibrium when $R_0>1$.

math.AP↗

arXiv2020

Asymptotic behavior of age-structured and delayed Lotka-Volterra models

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov functional that enables us to reduce the attractive set to either the nontrivial equilibrium or to a periodic solution. We then prove the asymptotic stability of the nontrivial equilibrium where, depending on the existence of the periodic trajectory, we make explicit the basin of attraction of the equilibrium. Finally, we prove that these results can be extended to the initial PDE problem.

math.AP↗

arXiv2019

Well-posedness and positivity property for a reaction-diffusion model of plankton communities, involving a rational nonlinearity with singularity

In this work, we consider a reaction-diffusion system, modeling the interaction between nutrients, phytoplanktons and zooplanktons. Using a semigroup approach in $L^2$, we prove global existence, uniqueness and positivity of the solutions. The Holling type 2 nonlinearities, i.e of rational type with singularity, are handled by providing estimates in $L^\infty$. The article finally exhibits some time asymptotics properties of the solutions.

math.AP↗

arXiv2017

Predicting the Evolution of Gene $ura3$ in the Yeast Saccharomyces Cerevisiae

Since the late `60s, various genome evolutionary models have been proposed to predict the evolution of a DNA sequence as the generations pass. Most of these models are based on nucleotides evolution, so they use a mutation matrix of size 4x4. They encompass for instance the well-known models of Jukes and Cantor, Kimura, and Tamura. By essence, all of these models relate the evolution of DNA sequences to the computation of the successive powers of a mutation matrix. To make this computation possible, particular forms for the mutation matrix are assumed, which are not compatible with mutation rates that have been recently obtained experimentally on gene ura3 of the Yeast Saccharomyces cerevisiae. Using this experimental study, authors of this paper have deduced a simple mutation matrice, compute the future evolution of the rate purine/pyrimidine for ura3, investigate the particular behavior of cytosines and thymines compared to purines, and simulate the evolution of each nucleotide.

q-bio.PE↗

arXiv2017

Criterion of positivity for semilinear problems with applications in biology

The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology.

math.AP↗

arXiv2016

Relaxing the Hypotheses of Symmetry and Time-Reversibility in Genome Evolutionary Models

Various genome evolutionary models have been proposed these last decades to predict the evolution of a DNA sequence over time, essentially described using a mutation matrix. By essence, all of these models relate the evolution of DNA sequences to the computation of the successive powers of the mutation matrix. To make this computation possible, hypotheses are assumed for the matrix, such as symmetry and time-reversibility, which are not compatible with mutation rates that have been recently obtained experimentally on genes ura3 and can1 of the Yeast Saccharomyces cerevisiae. In this work, authors investigate systematically the possibility to relax either the symmetry or the time-reversibility hypothesis of the mutation matrix, by investigating all the possible matrices of size 2*2 and 3*3. As an application example, the experimental study on the Yeast Saccharomyces cerevisiae has been used in order to deduce a simple mutation matrix, and to compute the future evolution of the rate purine/pyrimidine for $ura3$ on the one hand, and of the particular behavior of cytosines and thymines compared to purines on the other hand.

q-bio.BM↗

arXiv2016

Chaos in DNA Evolution

In this paper, we explain why the chaotic model (CM) of Bahi and Michel (2008) accurately simulates gene mutations over time. First, we demonstrate that the CM model is a truly chaotic one, as defined by Devaney. Then, we show that mutations occurring in gene mutations have the same chaotic dynamic, thus making the use of chaotic models relevant for genome evolution.

q-bio.GN↗