Affiliation:
1. Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, Mohammedia 20650, Morocco
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.
Subject
Applied Mathematics,Computational Mathematics,General Engineering
Reference44 articles.
1. Arruda, E.F., Das, S.S., Dias, C.M., and Pastore, D.H. (2021). Modelling and optimal control of multi strain epidemics, with application to COVID-19. PLoS ONE, 16.
2. Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: Application to COVID-19 pandemic;Khyar;Nonlinear Dyn.,2020
3. The global dynamics in a wild-type and drug-resistant HIV infection model with saturated incidence;Chen;Adv. Differ. Equ.,2020
4. Dynamics of a time-delayed two-strain epidemic model with general incidence rates;Amine;Chaos Solitons Fractals,2021
5. Optimal control for a time delay multi-strain tuberculosis fractional model: A numerical approach;Sweilam;IMA J. Math. Control. Inf.,2019
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献