Mathematical analysis of a delayed SEIRDS epidemics models: deterministic and stochastic approach

TL;DR

This paper analyzes how delays and stochastic factors influence the dynamics of SEIRDS epidemic models, providing mathematical insights into disease extinction, persistence, and the impact of immunity loss.

Contribution

It introduces a combined deterministic and stochastic analysis of delayed SEIRDS models, highlighting conditions for disease extinction and persistence.

Findings

Solutions exist and are unique for both models

Delay impacts the timing of epidemic waves

Stochastic factors influence disease persistence

Abstract

The primary goal of this research is to investigate the impact of delay on the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and Susceptible (SEIRDS) model, to which we add a stochastic term to account for uncertainty in COVID-19 parameter estimations. We run two models, one deterministic and one stochastic, and show that their solutions exist and are unique. We also numerically investigate the impact of immunity loss on the emerging time of a new wave, as well as the necessary condition for the extinction and persistence of the disease.