@article{fdi:010079849,
  title = {{C}oncentration estimates in a multi-host epidemiological model structured by phenotypic traits},
  author = {{B}urie, {J}. {B}. and {D}ucrot, {A}. and {G}riette, {Q}. and {R}ichard, {Q}uentin},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this work we consider a nonlocal system modelling the evolutionary adaptation of a pathogen within a multi-host population of plants. {H}ere we focus our analysis on the study of the stationary states. {W}e first discuss the existence of nontrivial equilibria using dynamical system arguments. {T}hen we introduce a small parameter 0 < epsilon << 1 that characterises the width of the mutation kernel, and we describe the asymptotic shape of steady states with respect to epsilon. {I}n particular, for epsilon -> 0 we show that the distribution of the pathogen approaches a singular measure concentrated on the maxima of fitness in each plant population. {T}his asymptotic description allows us to show the local stability of each of the positive steady states for 1, from which we deduce a uniqueness result for the nontrivial stationary states by means of a topological degree argument. {T}hese analyses rely on a careful investigation of the spectral properties of some nonlocal operators.},
  keywords = {{N}onlocal equation ; {S}teady state solutions ; {C}oncentration phenomenon ; {E}pidemiology ; {P}opulation genetics},
  booktitle = {},
  journal = {{J}ournal of {D}ifferential {E}quations},
  volume = {269},
  numero = {12},
  pages = {11492--11539},
  ISSN = {0022-0396},
  year = {2020},
  DOI = {10.1016/j.jde.2020.08.029},
  URL = {https://www.documentation.ird.fr/hor/fdi:010079849},
}