@article{fdi:010055960,
  title = {{R}eproductive numbers for nonautonomous spatially distributed periodic {SIS} models acting on two time scales},
  author = {{M}arva, {M}. and {B}ravo de la parra, {R}afael and {A}uger, {P}ierre},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this work we deal with a general class of spatially distributed periodic {SIS} epidemic models with two time scales. {W}e let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. {T}he existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated, system. {W}e derive global reproduction numbers governing the general spatially distributed nonautonomous system through the aggregated system. {W}e apply this result when the mass action law and the frequency dependent transmission law are considered. {C}omparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected.},
  keywords = {{N}onautonomous differential equations ; {SIS} model ; {T}wo patches model ; {T}wo time scales system approximate aggregation},
  booktitle = {},
  journal = {{A}cta {B}iotheoretica},
  volume = {60},
  numero = {1-2},
  pages = {139--154},
  ISSN = {0001-5342},
  year = {2012},
  DOI = {10.1007/s10441-011-9141-1},
  URL = {https://www.documentation.ird.fr/hor/fdi:010055960},
}