Qualitative properties of space-dependent SIR models with constant delay and their numerical solutions

TL;DR

This paper investigates a space-dependent SIR epidemic model with a fixed delay, analyzing its qualitative properties, proposing numerical schemes that preserve these features, and validating results through numerical experiments.

Contribution

The paper introduces a delay partial integro-differential equation for a space-dependent SIR model and develops numerical schemes that maintain its qualitative properties.

Findings

Numerical schemes preserve qualitative features with sufficiently small time steps.

The model exhibits biologically reasonable behaviors.

Numerical experiments confirm theoretical properties.

Abstract

In this article a space-dependent epidemic model equipped with a constant latency period is examined. We construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features. We propose some numerical schemes and show that by choosing the time step to be sufficiently small the schemes preserve the qualitative properties of the original continuous model. Finally, some numerical experiments are presented that confirm the aforementioned theoretical results.