# Concentration estimates in a multi-host epidemiological model structured by phenotypic traits

@article{Burie2019ConcentrationEI, title={Concentration estimates in a multi-host epidemiological model structured by phenotypic traits}, author={J. B. Burie and Arnaud Ducrot and Quentin Griette and Quentin Richard}, journal={arXiv: Analysis of PDEs}, year={2019} }

In this work we consider an epidemic system modelling the evolution of a spore-producing pathogen within a multi-host population of plants. Here we focus our analysis on the study of the stationary states. We first discuss the existence of such nontrivial states by using the theory of global attractors. Then we introduce a small parameter epsilon that characterises the width of the mutation kernel, and we describe the asymptotic shape of steady states with respect to epsilon. In particular, we… Expand

#### 3 Citations

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An integro-differential model with nonlocal effects of mutations to describe the evolutionary epidemiology of fungal plant pathogens in heterogeneous agricultural environments and investigates how the choice of quantitative resistances altering different pathogenicity traits impact the evolutionary dynamics of the pathogen population both at equilibrium and during transient epidemiological dynamics. Expand

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An integro-differential model with nonlocal effects of mutations is formulated to describe the evolutionary epidemiology dynamics of spore-producing pathogens in heterogeneous agricultural environments sharing a well-mixed pool of spores and shows that evolutionary attractors of the model coincide with local maxima of the only for traits involved in the sporulation curve. Expand

#### References

SHOWING 1-10 OF 41 REFERENCES

Steady state concentration for a phenotypic structured problem modeling the evolutionary epidemiology of spore producing pathogens

- Mathematics
- 2017

In this paper, we construct a model to describe the evolutionary epidemiology of spore producing asexual plant pathogens in a homogeneous host population. By considering the evolution in the space of… Expand

Dynamics of Concentration in a Population Model Structured by Age and a Phenotypical Trait

- Mathematics
- 2018

We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals… Expand

Asymptotic and transient behaviour for a nonlocal problem arising in population genetics

- Mathematics
- European Journal of Applied Mathematics
- 2018

This work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. First, we… Expand

Slow convergence to equilibrium for an evolutionary epidemiology integro-differential system

- Mathematics
- 2020

This work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. Using the… Expand

Evolution of pathogen traits in response to quantitative host resistance in heterogeneous environments

- Biology
- 2018

An integro-differential model with nonlocal effects of mutations to describe the evolutionary epidemiology of fungal plant pathogens in heterogeneous agricultural environments and investigates how the choice of quantitative resistances altering different pathogenicity traits impact the evolutionary dynamics of the pathogen population both at equilibrium and during transient epidemiological dynamics. Expand

The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach.

- Mathematics, Medicine
- Theoretical population biology
- 2005

The starting point is a selection-mutation equation describing the adaptive dynamics of a quantitative trait under the influence of an ecological feedback loop based on the assumption of small (but frequent) mutations, which is derived from a Hamilton-Jacobi equation. Expand

Asymptotics of steady states of a selection–mutation equation for small mutation rate

- Computer Science
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2013

It is proved existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. Expand

Travelling wave solutions for a non-local evolutionary-epidemic system

- Mathematics
- Journal of Differential Equations
- 2019

Abstract In this work we study the travelling wave solutions for a spatially distributed system of equations modelling the evolutionary epidemiology of plant-pathogen interaction. Here the mutation… Expand

STATIONARY DISTRIBUTIONS UNDER MUTATION- SELECTION BALANCE: STRUCTURE AND PROPERTIES

- Mathematics
- 1996

A general model for the evolution of the frequency distribution of types in a population under mutation and selection is derived and investigated. The approach is sufficiently general to subsume… Expand

Global Attractors and Steady States for Uniformly Persistent Dynamical Systems

- Computer Science, Mathematics
- SIAM J. Math. Anal.
- 2005

By appealing to the theory of global attractors on complete metric spaces, we obtain weaker sufficient conditions for the existence of interior global attractors for uniformly persistent dynamical… Expand