NDLI: Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on Two Time Scales

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Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on Two Time Scales

Content Provider	Springer Nature Link
Author	Marvá, M. Bravo de la Parra, R. Auger, P.
Copyright Year	2011
Abstract	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.
Starting Page	139
Ending Page	154
Page Count	16
File Format	PDF
ISSN	00015342
Journal	Acta Biotheoretica
Volume Number	60
Issue Number	1-2
e-ISSN	15728358
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-12-07
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonautonomous differential equations SIS model Two patches model Two time scales system approximate aggregation Evolutionary Biology Philosophy of Biology
Content Type	Text
Resource Type	Article
Subject	Philosophy Applied Mathematics Medicine Biochemistry, Genetics and Molecular Biology Environmental Science Agricultural and Biological Sciences

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