Nonlocal finite difference discretization of a class of renewal equation models for epidemics

Math Biosci Eng. 2023 May 6;20(7):11656-11675. doi: 10.3934/mbe.2023518.

Abstract

In this paper we consider a non-standard discretization to a Volterra integro-differential system which includes a number of age-of-infection models in the literature. The aim is to provide a general framework to analyze the proposed scheme for the numerical solution of a class of problems whose continuous dynamic is well known in the literature and allow a deeper analysis in cases where the theory lacks.

Keywords: Volterra integral equations; asymptotic dynamics; epidemic models; non-standard difference scheme.