Effect of the number of patches in a multi-patch SIRS model with fast migration on the basic reproduction rate

Authored by Etienne Kouokam, Pierre Auger, Hassan Hbid, Maurice Tchuente

Date Published: 2008

DOI: 10.1007/s10441-008-9036-y

Sponsors: Institut de Recherche pour le Développement (IRD)

Platforms: No platforms listed

Model Documentation: Other Narrative Flow charts Mathematical description

Model Code URLs: Model code not found

Abstract

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 (P > 2). 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.

Tags

Population-dynamics Persistence Frequency