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Related Experiment Video

Updated: Nov 3, 2025

A Delayed Inoculation Model of Chronic Pseudomonas aeruginosa Wound Infection

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Published on: February 20, 2020

A Diffusive Sveir Epidemic Model with Time Delay and General Incidence.

Jinling Zhou¹, Xinsheng Ma¹, Yu Yang²

¹Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310023 China.

Acta Mathematica Scientia = Shu Xue Wu Li Xue Bao

|June 7, 2021

Summary

A prolonged time delay in a diffusive SVEIR model can eliminate infectiousness. This study establishes threshold dynamics and proves global stability of equilibria using a Nonstandard Finite Difference scheme.

Keywords:

Lyapunov function SVEIR model nonstandard finite difference method vaccination

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Area of Science:

Mathematical modeling of infectious diseases
Epidemiology
Dynamical systems

Background:

The spread of infectious diseases is a significant public health concern.
Mathematical models are crucial for understanding disease dynamics and control.

Purpose of the Study:

To analyze a delayed diffusive SVEIR (Susceptible-Viral-Infected-Exposed-Recovered) model.
To investigate the impact of time delays on disease transmission and stability.

Main Methods:

Establishment of threshold dynamics for the SVEIR model.
Discretization of the continuous model using a Nonstandard Finite Difference (NSFD) scheme.
Application of Lyapunov functions to prove global stability of equilibria.

Main Results:

The threshold dynamics of the delayed diffusive SVEIR model were successfully established.
Global stability of the model's equilibria was proven using Lyapunov functions.
Numerical simulations validated the theoretical findings.

Conclusions:

Time delays in disease models can significantly alter epidemiological outcomes.
Prolonged time delays were shown to potentially lead to the elimination of infectiousness.
The NSFD scheme provides a robust method for discretizing and analyzing such models.