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.

Threshold behaviour of SIR epidemic model with age structure and immigration / Franceschetti, Andrea; Pugliese, Andrea. - ELETTRONICO. - (2007), pp. 1-20.

Threshold behaviour of SIR epidemic model with age structure and immigration

Pugliese, Andrea
2007-01-01

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.
2007
Trento
Università degli Studi di Trento - Dipartimento di Matematica
Threshold behaviour of SIR epidemic model with age structure and immigration / Franceschetti, Andrea; Pugliese, Andrea. - ELETTRONICO. - (2007), pp. 1-20.
Franceschetti, Andrea; Pugliese, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/359600
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