TY  - UNPB
A1  - Franceschetti, Andrea
A1  - Pugliese, Andrea
ID  - elediasc12431
AV  - public
TI  - Threshold behaviour of SIR epidemic model with age structure and immigration
Y1  - 2007/02//
UR  - http://www.eledia.org/students-reports/431/
N2  - 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.
ER  -