Open AccessA non-standard numerical scheme for an age-of-infection epidemic model
Author(s) -
Eleonora Messina,
Mario Pezzella,
Antonia Vecchio
Publication year - 2022
Publication title -
journal of computational dynamics
Language(s) - English
Resource type - Journals
eISSN - 2158-2505
pISSN - 2158-2491
DOI - 10.3934/jcd.2021029
Subject(s) - mathematics , convergence (economics) , term (time) , zero (linguistics) , differential equation , mathematical analysis , physics , linguistics , philosophy , quantum mechanics , economics , economic growth
We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the equation. The study of convergence properties and the analysis of the qualitative behavior of the numerical solution show that it preserves all the basic properties of the continuous model with no restrictive conditions on the step-length \begin{document}$ h $\end{document} of integration and that it recovers the continuous dynamic as \begin{document}$ h $\end{document} tends to zero.