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Related Experiment Video

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Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

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Published on: June 15, 2022

Threshold dynamics of difference equations for SEIR model with nonlinear incidence function and infinite delay.

Soufiane Bentout^1,2, Salih Djilali^1,3, Sunil Kumar^4,5

¹Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria.

European Physical Journal Plus

|June 2, 2021

Summary

This study analyzes an age-structured SEIR model with nonlinear incidence, proving global stability for disease-free and endemic states. Numerical simulations confirm the theoretical findings on infection persistence and stability.

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Area of Science:

Mathematical epidemiology
Dynamical systems theory

Background:

Age-structured SEIR models are crucial for understanding disease dynamics.
Nonlinear incidence functionals (NIF) introduce complex threshold behaviors.
Global asymptotic stability (GAS) analysis is essential for predicting long-term disease outcomes.

Purpose of the Study:

To investigate the global conduct of an age-structured SEIR system with NIF.
To analyze the global asymptotic stability (GAS) of the disease-free equilibrium (DFE) and endemic equilibrium (EE).
To establish conditions for infection persistence.

Main Methods:

Rewriting the SEIR model as difference equations with infinite delay using the characteristic method.
Employing a Lyapunov functional (LF) to prove GAS for the DFE.
Utilizing the total trajectory method to bypass local equilibrium analysis.
Applying weakly persistence theory for the EE analysis.

Main Results:

Demonstrated threshold behavior in the SEIR model with NIF.
Established conditions for the global asymptotic stability (GAS) of the disease-free equilibrium (DFE).
Proved infection persistence and the GAS of the endemic equilibrium (EE) under specific conditions.

Conclusions:

The study provides a comprehensive analysis of an age-structured SEIR model with NIF.
Theoretical results on stability and persistence are supported by numerical simulations.
The findings contribute to a deeper understanding of epidemic dynamics and control strategies.