Threshold behaviour of a SIR epidemic model with age structure and immigration |
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Authors: | Andrea Franceschetti Andrea Pugliese |
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Institution: | (1) Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050 Povo (TN), Italy |
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Abstract: | We consider a SIR age-structured model with immigration of infectives in all epidemiological compartments; the population
is assumed to be 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
by the Italian demographic situation, that illustrate the threshold-like behaviour, and other features of the stationary solutions
and of the transient.
Supported in part by FIRB project RBAU01K7M2 “Metodi dell’Analisi Matematica in Biologia, Medicina e Ambiente” of the Italian
Ministero Istruzione Università e Ricerca |
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Keywords: | Age structured epidemic model Immigration Below replacement fertility Quasi-threshold theorem Fixed points of positive operators |
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