A non-standard numerical scheme for an age-of-infection epidemic model

TL;DR

This paper introduces a novel numerical scheme for age-of-infection epidemic models that accurately approximates integro-differential equations while preserving key properties of the continuous model without restrictive step-size conditions.

Contribution

It presents a non-standard finite differences method for integro-differential equations in epidemic modeling, ensuring convergence and qualitative property preservation.

Findings

The scheme converges to the continuous solution as step size decreases.

It preserves the basic properties of the epidemic model.

No restrictive conditions on step size are required.

Abstract

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 $h$ of integration and that it recovers the continuous dynamic as $h$ tends to zero.