eprintid: 431
rev_number: 4
eprint_status: archive
userid: 5
dir: disk0/00/00/04/31
datestamp: 2007-04-19
lastmod: 2013-07-01 14:05:16
status_changed: 2013-07-01 14:05:16
type: techreport
metadata_visibility: show
item_issues_count: 0
creators_name: Franceschetti, Andrea
creators_name: Pugliese, Andrea
title: Threshold behaviour of SIR epidemic model with age structure and immigration
ispublished: unpub
subjects: TU
full_text_status: public
abstract: We consider a SIR age-structured model with immigration of infectives in all epidemiological compartments; the population is supposed in demographic equilibrium between below-replacement fertility and immigration; the spread of the infection occurs through a general age-dependent kernel. We analyse the equations for steady states; because of immigration of infectives a steady state with a positive density of infectives always exists; however, a quasi-threshold theorem is proved, in the sense that, below the threshold, the density of infectives is close to 0, while it is away from 0, above the threshold; furthermore, conditions that guarantee uniqueness of steady states are obtained. Finally, we present some numerical examples, inspired to the Italian demographic situation, that illustrate the threshold-like behaviour, and other features of the stationary solutions and of the transient.
date: 2007-02
date_type: published
institution: University of Trento
department: matematica
refereed: FALSE
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citation:   Franceschetti, Andrea and Pugliese, Andrea  (2007) Threshold behaviour of SIR epidemic model with age structure and immigration.  [Technical Report]    (Unpublished)  
document_url: http://www.eledia.org/students-reports/431/1/UTM710.pdf