Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction Rate
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Acta Biotheoretica 56 (1-2):75-86 (2008)
We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than the 1 patch one. We extend this result to a linear chain of P patches . These results are illustrated by some examples for which numerical integration of the system of ordinary differential equations is performed. Simulations of an individual based model implemented with a multi-agent system are also carried out
|Keywords||Philosophy Evolutionary Biology Philosophy of Biology|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
S. Charles, R. Bravo de la Parra, J. P. Mallet, H. Persat & P. Auger (1998). Population Dynamics Modelling in an Hierarchical Arborescent River Network: An Attempt with Salmo Trutta. Acta Biotheoretica 46 (3):223-234.
C. P. Bhunu, W. Garira & G. Magombedze (2009). Mathematical Analysis of a Two Strain Hiv/Aids Model with Antiretroviral Treatment. Acta Biotheoretica 57 (3):361-381.
R. Mchich, P. Auger & N. Raïssi (2000). The Dynamics of a Fish Stock Exploited in Two Fishing Zones. Acta Biotheoretica 48 (3-4):207-218.
J.-C. Poggiale, P. Auger, D. Nérini, C. Manté & F. Gilbert (2005). Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model. Acta Biotheoretica 53 (4):359-370.
Ángeles Rincón, Juan Antonio Alonso & Luis Sanz (2009). Reduction of Supercritical Multiregional Stochastic Models with Fast Migration. Acta Biotheoretica 57 (4):479-500.
Karine Chalvet-Monfray, Marc Artzrouni, Jean-Paul Gouteux, Pierre Auger & Philippe Sabatier (1998). A Two-Patch Model of Gambian Sleeping Sickness: Application to Vector Control Strategies in a Village and Plantations. Acta Biotheoretica 46 (3):207-222.
Peter Antonelli & Pierre Auger (1995). Corals and Starfish Devastation of the Great Barrier Reef: Aggregation Methods. Acta Biotheoretica 43 (4):481-493.
Pierre Auger & Jean-Christophe Poggiale (1996). Aggregation and Emergence in Hierarchically Organized Systems: Population Dynamics. Acta Biotheoretica 44 (3-4):301-316.
Rachid Mchich, Amal Bergam & Nadia Raïssi (2005). Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model. Acta Biotheoretica 53 (4):331-340.
Added to index2009-01-28
Total downloads11 ( #301,028 of 1,793,164 )
Recent downloads (6 months)3 ( #280,900 of 1,793,164 )
How can I increase my downloads?