@unpublished{elediasc12431,
            year = {2007},
           title = {Threshold behaviour of SIR epidemic model with age structure and immigration},
           month = {February},
          author = {Andrea Franceschetti and Andrea Pugliese},
             url = {http://www.eledia.org/students-reports/431/},
        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.}
}