• Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

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Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

Verlag der Österreichischen Akademie der Wissenschaften
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ETNA - Electronic Transactions on Numerical Analysis



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
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A stable numerical method for integral epidemic models with behavioral changes in contact patterns

    Bruno Buonomo, Eleonora Messina, Claudia Panico, Antonia Vecchio

ETNA - Electronic Transactions on Numerical Analysis, pp. 137-156, 2024/11/11

doi: 10.1553/etna_vol61s137

doi: 10.1553/etna_vol61s137


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doi:10.1553/etna_vol61s137



doi:10.1553/etna_vol61s137

Abstract

We propose a non-standard numerical method for the solution of a system of integro-differential equations describing an epidemic of an infectious disease
with behavioral changes in contact patterns. The method is constructed in order to preserve the key characteristics of the model, like the positivity of solutions, the existence of equilibria, and asymptotic behavior. We prove that
the numerical solution converges to the exact solution as the step size $h$ of the discretization tends to zero. Furthermore, the method is first-order accurate, meaning that the error in the discretization is $O(h)$, it is linearly
implicit, and it preserves all the properties of the continuous problem, unconditionally with respect to $h$. Numerical simulations show all these properties and confirm, also by means of a case-study, that the method provides
correct qualitative information at a low computational cost.

Keywords: epidemic models, integro-differential equations, non-standard finite difference scheme, discrete models, perturbation theory