Abstract
We formulate a model describing the dynamics for the spatial propagation of an SIS epidemic within a population, with age structure, living in an environment divided into two sites. An analysis of the model is given. We prove the existence of a unique disease free equilibrium (DFE) and its (local and global) stability. Further, we assume that fast infection processes and fast migration processes take place in the above-mentioned model; i.e. such processes last only a few days (less than a week). In opposition to such processes, demographic processes such as birth, death and maturation last quite a lot of years. Such a gap between the time scales gives rise to a multiple time scales model, in particular a singularly perturbed model. Through a singular perturbation analysis, based on Tikhonov theorem, we prove that for certain classes of initial conditions the nonlinear perturbed model can be approximated with very good accuracy by lower-dimensional linear models.
Published Version
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