Tin Nwe Aye | Searcharxiv

arXiv2025

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

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.

math.NA↗

arXiv2025

Analyzing Smoothness and Dynamics in an SEIR$^{\text{T}}$R$^{\text{P}}$D Endemic Model with Distributed Delays

This article explores the properties of an SEIR$^{\text{T}}$R$^{\text{P}}$D endemic model expressed through delay-differential equations with distributed delays for latency and temporary immunity. Our research delves into the variability of latent periods and immunity durations across diseases, in particular, we introduce a class of delays defined by continuous integral kernels with compact support. The main result of the paper is a kind of smoothening property which the solution function posesses under mild conditions of the system parameter functions. Also, boundedness and non-negativity is proved. Numerical simulations indicates that the continuous model can be approximated with a discrete lag endemic models. The study contributes to understanding infectious disease dynamics and provides insights into the numerical approximation of exact solution for different delay scenarios.

math.NA↗