Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation

Eleonora Messina

doi:10.3934/proc.2015.0826

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2015, Volume 2015: 826-834. Doi: 10.3934/proc.2015.0826 open access

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Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation

Eleonora Messina^1,

1.
Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples

Received: August 31, 2014

Revised: June 30, 2015

Published: October 2015

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Abstract

We consider a SIS epidemic model based on a Volterra integral equation and we compare the dynamical behavior of the analytical solution and its numerical approximation obtained by direct quadrature methods. We prove that, under suitable assumptions, the numerical scheme preserves the qualitative properties of the continuous equation and we show that, as the stepsize tends to zero, the numerical bifurcation points tend to the continuous ones.

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Mathematics Subject Classification: Primary: 45D05, 65R20; Secondary: 65L20.

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