Persistence-time estimation for some stochastic SIS epidemic models

Francisco de la  Hoz; Anna  Doubova; Fernando  Vadillo

doi:10.3934/dcdsb.2015.20.2933

Article Contents

2015, Volume 20, Issue 9: 2933-2947. Doi: 10.3934/dcdsb.2015.20.2933

This issue Previous Article Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities Next Article Kurzweil integral representation of interacting Prandtl-Ishlinskii operators

Persistence-time estimation for some stochastic SIS epidemic models

1.
Department of Applied Mathematics and Statistics and Operations Research, University of the Basque Country UPV/EHU
2.
Department of Dierential Equations and Numerical Analysis, University of Sevilla

Received: June 30, 2014

Revised: June 30, 2015

Published: October 2015

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Abstract

In this paper, we study two stochastic SIS epidemic models: the first one with a constant population size, and the second one with a death factor. We analyze persistence and extinction behaviors for these models. The persistence time depends on the initial population size and satisfies a stationary backward Kolmogorov differential equation, which is a linear second-order partial differential equation with variable degenerate coefficients. We solve this equation numerically using a classical finite element method. We give computational evidence that the importance of understanding the dynamics of both the deterministic and the stochastic epidemic models is due to the numerical approximations to the mean persistence time. This can give more information about the model and may perhaps explain strange behaviors, such as the differences between the deterministic model and the stochastic one for long times.

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Mathematics Subject Classification: 60H10, 92B05, 65N30.

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