Convergence Analysis of an Endemic Time Delay Model Using Dirac and Radon Measures

TL;DR

This paper analyzes the convergence of an endemic disease model incorporating Dirac and Radon measures with delays, demonstrating that discrete models can approximate continuous ones efficiently, reducing simulation time.

Contribution

It introduces a novel convergence analysis for an endemic model with Dirac and Radon measures, bridging continuous and discrete delay models.

Findings

Discrete endemic models approximate continuous models effectively.

Numerical simulations are faster than exact solutions.

The model captures latency and immunity dynamics accurately.

Abstract

This article explores the convergence properties of an $SLIR^\text{T}R^\text{P}D$ endemic model, incorporating Dirac and Radon measures, alongside distributed delays to represent latency and temporary immunity. A class of delays is defined for both continuous and discrete endemic models using continuous integral kernels with compact support and discrete terms expressed through Dirac and Radon measures. Numerical results show that the continuous model can be approximated by a discrete lag endemic model. Furthermore, the simulation time for the numerical solution is significantly shorter than that for the exact solution.