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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: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 137-156, 2024/11/11
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