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P. Auger, R. Parra, J. Poggiale, E. Sánchez, L. Sanz (2008)
Aggregation methods in dynamical systems and applications in population and community dynamicsPhysics of Life Reviews, 5
F. Verhulst (2007)
Singular perturbation methods for slow–fast dynamicsNonlinear Dynamics, 50
P. Auger, Etienne Kouokam, G. Sallet, M. Tchuenté, B. Tsanou (2008)
The Ross-Macdonald model in a patchy environment.Mathematical biosciences, 216 2
F. Hoppensteadt (2010)
Quasi-Static State Analysis of Differential, Difference, Integral, and Gradient Systems
H. Thieme (2003)
Mathematics in Population Biology
M. Martcheva (2009)
A non-autonomous multi-strain SIS epidemic modelJournal of Biological Dynamics, 3
Junling Ma, Zhien Ma (2005)
Epidemic threshold conditions for seasonally forced seir models.Mathematical biosciences and engineering : MBE, 3 1
Etienne Kouokam, P. Auger, Hassan Hbid, M. Tchuenté (2008)
Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction RateActa Biotheoretica, 56
Y. Iwasa, V. Andreasen, S. Levin (1987)
Aggregation in model ecosystems. I. Perfect aggregationEcological Modelling, 37
P. Auger, R. Parra, J. Poggiale, E. Sánchez, T. Nguyen-Huu (2008)
Aggregation of Variables and Applications to Population Dynamics
S. Chow, J. Hale (1996)
Methods of Bifurcation Theory
Neil Fenichel (1971)
Persistence and Smoothness of Invariant Manifolds for FlowsIndiana University Mathematics Journal, 21
F. Verhulst (2010)
Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics
H. McCallum, N. Barlow, J. Hone (2001)
How should pathogen transmission be modelled?Trends in ecology & evolution, 16 6
F. Hoppensteadt (1992)
Analysis and simulation of chaotic systems
A. Lloyd, V. Jansen (2004)
Spatiotemporal dynamics of epidemics: synchrony in metapopulation models.Mathematical biosciences, 188
H. Thieme (2000)
Uniform persistence and permanence for non-autonomous semiflows in population biology.Mathematical biosciences, 166 2
Julien Arino, Jonathan Davis, D. Hartley, R. Jordan, Joy Miller, P. Driessche (2005)
A multi-species epidemic model with spatial dynamics.Mathematical medicine and biology : a journal of the IMA, 22 2
Y Iwasa, V Andreasen, S Levin (1989)
Aggregation in model ecosystems II: approximate aggregationJ Math App Med Biol, 6
Julien Arino, R. Jordan, P. Driessche (2007)
Quarantine in a multi-species epidemic model with spatial dynamics.Mathematical biosciences, 206 1
Y. Iwasa, S. Levin, V. Andreasen (1989)
Aggregation in Model Ecosystems II. Approximate AggregationMathematical Medicine and Biology-a Journal of The Ima, 6
P Auger, E Kouokam, G Sallet, M Tchuente, B Tsanou (2008)
Vector-borne diseases with spatial dynamics: the Ross-Macdonald model in a patchy environmentMath Biosci, 216
F. Hoppensteadt (1966)
Singular perturbations on the infinite intervalTransactions of the American Mathematical Society, 123
M. Farkas (1994)
Periodic Motions
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.
Acta Biotheoretica – Springer Journals
Published: Dec 7, 2011
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