A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis

The paper investigates a spatio-temporal SEIR epidemic model on a global level with fractional order. It employs four partial differential equations incorporating fractional derivatives and account for diffusion to characterize infection dynamics. By applying fixed-point theorem results, the paper e...

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Main Authors: Sara Soulaimani, Abdelilah Kaddar, Fathalla A. Rihan
Format: Article
Language:English
Published: Elsevier 2024-12-01
Series:Scientific African
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Online Access:http://www.sciencedirect.com/science/article/pii/S2468227624002916
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author Sara Soulaimani
Abdelilah Kaddar
Fathalla A. Rihan
author_facet Sara Soulaimani
Abdelilah Kaddar
Fathalla A. Rihan
author_sort Sara Soulaimani
collection DOAJ
description The paper investigates a spatio-temporal SEIR epidemic model on a global level with fractional order. It employs four partial differential equations incorporating fractional derivatives and account for diffusion to characterize infection dynamics. By applying fixed-point theorem results, the paper establishes the existence, uniqueness, and boundedness of the solution. Equilibrium points are determined based on vaccination values and the basic reproduction number R0. Global stability of each equilibrium is confirmed using the Lyapunov direct method. Through simulations with a predictor–corrector algorithm, key insights into epidemiological dynamics are provided, elucidating the impact of vaccination on reducing disease transmission and altering R0. Trajectories of various compartments closely align with theoretical equilibrium points, affirming the model’s predictive precision. Furthermore, simulations indicate the potential for attaining disease-free equilibria with heightened vaccination rates, underscoring the pivotal role of vaccination strategies in epidemic control and disease eradication. It was shown that the fractional derivative order has no effect on the equilibrium stability but rather only on the convergence speed towards the equilibrium points.
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spelling doaj-art-c1275ac84090461f8ec9c30af7e001132025-08-20T02:40:07ZengElsevierScientific African2468-22762024-12-0126e0234910.1016/j.sciaf.2024.e02349A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysisSara Soulaimani0Abdelilah Kaddar1Fathalla A. Rihan2Chouaib Doukkali University, Faculty of Sciences El Jadida, Department of Mathematics, LabSIPE laboratory, El Jadida, Morocco; Corresponding author.Chouaib Doukkali University of El Jadida, Natl Sch App Sci , Sci Engineer Lab Energy, El Jadida, MoroccoDepartment of Mathematical Sciences, College of Science, UAE University, 15551 Al-Ain, United Arab EmiratesThe paper investigates a spatio-temporal SEIR epidemic model on a global level with fractional order. It employs four partial differential equations incorporating fractional derivatives and account for diffusion to characterize infection dynamics. By applying fixed-point theorem results, the paper establishes the existence, uniqueness, and boundedness of the solution. Equilibrium points are determined based on vaccination values and the basic reproduction number R0. Global stability of each equilibrium is confirmed using the Lyapunov direct method. Through simulations with a predictor–corrector algorithm, key insights into epidemiological dynamics are provided, elucidating the impact of vaccination on reducing disease transmission and altering R0. Trajectories of various compartments closely align with theoretical equilibrium points, affirming the model’s predictive precision. Furthermore, simulations indicate the potential for attaining disease-free equilibria with heightened vaccination rates, underscoring the pivotal role of vaccination strategies in epidemic control and disease eradication. It was shown that the fractional derivative order has no effect on the equilibrium stability but rather only on the convergence speed towards the equilibrium points.http://www.sciencedirect.com/science/article/pii/S2468227624002916Global dynamicsTime-fractionalReaction–diffusion systemsSpatio-temporal SEIR epidemic modelGeneral incidence functionLyapunov functional
spellingShingle Sara Soulaimani
Abdelilah Kaddar
Fathalla A. Rihan
A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis
Scientific African
Global dynamics
Time-fractional
Reaction–diffusion systems
Spatio-temporal SEIR epidemic model
General incidence function
Lyapunov functional
title A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis
title_full A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis
title_fullStr A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis
title_full_unstemmed A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis
title_short A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis
title_sort spatio temporal infection epidemic model with fractional order general incidence and vaccination analysis
topic Global dynamics
Time-fractional
Reaction–diffusion systems
Spatio-temporal SEIR epidemic model
General incidence function
Lyapunov functional
url http://www.sciencedirect.com/science/article/pii/S2468227624002916
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