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Global Stability of Multi-Strain SEIR Epidemic Model with Vaccination Strategy

Authors :
Zakaria Yaagoub
Karam Allali
Source :
Mathematical and Computational Applications, Vol 28, Iss 1, p 9 (2023)
Publication Year :
2023
Publisher :
MDPI AG, 2023.

Abstract

A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This model is represented by a system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated individuals, strain-1-exposed individuals, strain-2-exposed individuals, strain-3-exposed individuals, strain-1-infected individuals, strain-2-infected individuals, strain-3-infected individuals, and recovered individuals. We start our analysis of this model by establishing the existence, positivity, and boundedness of all the solutions. In order to show global stability, the model has five equilibrium points: The first one stands for the disease-free equilibrium, the second stands for the strain-1 endemic equilibrium, the third one describes the strain-2 equilibrium, the fourth one represents the strain-3 equilibrium point, and the last one is called the total endemic equilibrium. We establish the global stability of each equilibrium point using some suitable Lyapunov function. This stability depends on the strain-1 reproduction number R01, the strain-2 basic reproduction number R02, and the strain-3 reproduction number R03. Numerical simulations are given to confirm our theoretical results. It is shown that in order to eradicate the infection, the basic reproduction numbers of all the strains must be less than unity.

Details

Language :
English
ISSN :
22978747 and 1300686X
Volume :
28
Issue :
1
Database :
Directory of Open Access Journals
Journal :
Mathematical and Computational Applications
Publication Type :
Academic Journal
Accession number :
edsdoj.6283c7faf3ae4abda1b2ec4e050ba00a
Document Type :
article
Full Text :
https://doi.org/10.3390/mca28010009