Threshold behaviour of SIR epidemic model with age structure and immigration

Franceschetti, Andrea and Pugliese, Andrea (2007) Threshold behaviour of SIR epidemic model with age structure and immigration. UNSPECIFIED. (Unpublished)

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    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.

    Item Type: Departmental Technical Report
    Department or Research center: Mathematics
    Subjects: Q Science > QA Mathematics > QA276 Mathematical Statistics
    Report Number: UTM 710, February 2007
    Repository staff approval on: 19 Apr 2007

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