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Roger Pettersson: Two different epidemic models with the same limiting ODE

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Föreläsare/Lecturer

Roger Pettersson, docent i matematik, institutionen för matematik, Linnéuniversitetet

Titel/Title

Two different epidemic models with the same limiting ODE

Sammanfattning/Abstract

We consider one epidemic model describing the fraction of infected individuals driven by a Wiener process, as suggested in Iacus (2008). The model involves a transmission rate, a recovery rate, a transmission rate from an external source, and a population density parameter. Depending on different choices of the parameters, different properties of a solution is obtained, such as instantanteous reflection or absorbance and asymptotics in time.

We also compare with a diffusion approximation of a related discrete-valued birth-death process in continuous time. The Iacus model and the diffusion approximation are different but coincide for large population densities with the same limiting ordinary differential equation.

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