%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Marva, M.
%A Bravo de la parra, Rafael
%A Auger, Pierre
%T Reproductive numbers for nonautonomous spatially distributed periodic SIS models acting on two time scales
%D 2012
%L fdi:010055960
%G ENG
%J Acta Biotheoretica
%@ 0001-5342
%K Nonautonomous differential equations ; SIS model ; Two patches model ; Two time scales system approximate aggregation
%M ISI:000305210000010
%N 1-2
%P 139-154
%R 10.1007/s10441-011-9141-1
%U https://www.documentation.ird.fr/hor/fdi:010055960
%> https://www.documentation.ird.fr/intranet/publi/2012/07/010055960.pdf
%V 60
%W Horizon (IRD)
%X In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The 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. We derive global reproduction numbers governing the general spatially distributed nonautonomous system through the aggregated system. We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing 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.
%$ 020