?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fwww.eledia.org%2Fstudents-reports%2F431%2F&rft.title=Threshold+behaviour+of+SIR+epidemic+model+with+age+structure+and+immigration&rft.creator=Franceschetti%2C+Andrea&rft.creator=Pugliese%2C+Andrea&rft.subject=TU+Technical+Reports+and+Publications&rft.description=We+consider+a+SIR+age-structured+model+with+immigration+of+infectives+in+all+epidemiological+compartments%3B+the+population+is+supposed+in+demographic+equilibrium+between+below-replacement+fertility+and+immigration%3B+the+spread+of+the+infection+occurs+through+a+general+age-dependent+kernel.+We+analyse+the+equations+for+steady+states%3B+because+of+immigration+of+infectives+a+steady+state+with+a+positive+density+of+infectives+always+exists%3B+however%2C+a+quasi-threshold+theorem+is+proved%2C+in+the+sense+that%2C+below+the+threshold%2C+the+density+of+infectives+is+close+to+0%2C+while+it+is+away+from+0%2C+above+the+threshold%3B+furthermore%2C+conditions+that+guarantee+uniqueness+of+steady+states+are+obtained.+Finally%2C+we+present+some+numerical+examples%2C+inspired+to+the+Italian+demographic+situation%2C+that+illustrate+the+threshold-like+behaviour%2C+and+other+features+of+the+stationary+solutions+and+of+the+transient.&rft.date=2007-02&rft.type=Technical+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fwww.eledia.org%2Fstudents-reports%2F431%2F1%2FUTM710.pdf&rft.identifier=++Franceschetti%2C+Andrea+and+Pugliese%2C+Andrea++(2007)+Threshold+behaviour+of+SIR+epidemic+model+with+age+structure+and+immigration.++%5BTechnical+Report%5D++++(Unpublished)++