Multiscale Analysis for a Vector-Borne Epidemic Model

Details Multiscale Analysis for a Vector-Borne Epidemic Model Multiscale Analysis for a Vector-Borne Epidemic Model

2011-08-09

arxiv.org/abs/1108.1999v1

Biology

Quantitative Biology

Populations and Evolution

Scientific paper

We investigate a classical mass-action model for diseases transmitted by arbovirus. Most traditional studies have focused on global stability issues and oscillatory behaviour. Here, we take a different view and we study the dynamics of the model, under the hypothesis that the typical timescale for the host and the vector are distinct. In this way, two asymptotic dynamics naturally appear: the fast host dynamics and the fast vector dynamics. The former yields, at leading order, a SIR model for the hosts, but with a modified incidence rate. Thus, the vector disappears from the model, and the dynamics is similar to a directly contagious disease. The latter yields a SI model for the vectors, with the hosts disappearing from the model. Numerical results show the performance of the approximation, and a rigorous proof validates the reduced models.

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