Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel

Abstract Vector-borne infections impose a significant burden on global health systems and economies due to their widespread impact and the substantial resources required for prevention, control, and treatment efforts. In this work, we formulate a mathematical model for the transmission dynamics of a...

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Main Authors: Nekmat Ullah, Zahir Shah, Rashid Jan, Narcisa Vrinceanu, Muhammad Farhan, Elisabeta Antonescu
Format: Article
Language:English
Published: Nature Portfolio 2025-02-01
Series:Scientific Reports
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Online Access:https://doi.org/10.1038/s41598-025-90182-1
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author Nekmat Ullah
Zahir Shah
Rashid Jan
Narcisa Vrinceanu
Muhammad Farhan
Elisabeta Antonescu
author_facet Nekmat Ullah
Zahir Shah
Rashid Jan
Narcisa Vrinceanu
Muhammad Farhan
Elisabeta Antonescu
author_sort Nekmat Ullah
collection DOAJ
description Abstract Vector-borne infections impose a significant burden on global health systems and economies due to their widespread impact and the substantial resources required for prevention, control, and treatment efforts. In this work, we formulate a mathematical model for the transmission dynamics of a vector-borne infection with the effect of vaccination through the Atangana-Baleanu derivative. The solutions of the model are positive and bounded for positive initial values of the state variable. We presented the basic concept and theory of fractional calculus for the analysis of the model. We determine the threshold parameter, denoted by $$\mathcal {R}_0$$ , using the next-generation matrix method. The local asymptotic stability of the system at the disease-free equilibrium is analyzed. To establish the existence of solutions for the proposed model, we employ fixed-point theory. A numerical scheme is developed to visualize the system’s dynamical behavior under varying input parameters. Numerical simulations are conducted to illustrate how these parameters influence the dynamics of the system. The results highlight key factors affecting the transmission and control of vector-borne diseases, offering insights into strategies for prevention and mitigation.
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spelling doaj-art-b4cd7160c5414801a3af1ebec00db1c32025-08-20T02:15:00ZengNature PortfolioScientific Reports2045-23222025-02-0115111610.1038/s41598-025-90182-1Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernelNekmat Ullah0Zahir Shah1Rashid Jan2Narcisa Vrinceanu3Muhammad Farhan4Elisabeta Antonescu5Department of Mathematical Sciences, University of Lakki MarwatDepartment of Mathematical Sciences, University of Lakki MarwatInstitute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITENDepartment of Mathematics, College of Science, King Saud UniversitySchool of Mathematical Science, Yangzhou UniversityPreclinical Department Faculty of Medicine, Lucian Blaga University of SibiuAbstract Vector-borne infections impose a significant burden on global health systems and economies due to their widespread impact and the substantial resources required for prevention, control, and treatment efforts. In this work, we formulate a mathematical model for the transmission dynamics of a vector-borne infection with the effect of vaccination through the Atangana-Baleanu derivative. The solutions of the model are positive and bounded for positive initial values of the state variable. We presented the basic concept and theory of fractional calculus for the analysis of the model. We determine the threshold parameter, denoted by $$\mathcal {R}_0$$ , using the next-generation matrix method. The local asymptotic stability of the system at the disease-free equilibrium is analyzed. To establish the existence of solutions for the proposed model, we employ fixed-point theory. A numerical scheme is developed to visualize the system’s dynamical behavior under varying input parameters. Numerical simulations are conducted to illustrate how these parameters influence the dynamics of the system. The results highlight key factors affecting the transmission and control of vector-borne diseases, offering insights into strategies for prevention and mitigation.https://doi.org/10.1038/s41598-025-90182-1Fractional calculusVector-borne infectionMathematical modelExistence theoryFixed-point theoremNumerical analysis
spellingShingle Nekmat Ullah
Zahir Shah
Rashid Jan
Narcisa Vrinceanu
Muhammad Farhan
Elisabeta Antonescu
Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel
Scientific Reports
Fractional calculus
Vector-borne infection
Mathematical model
Existence theory
Fixed-point theorem
Numerical analysis
title Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel
title_full Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel
title_fullStr Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel
title_full_unstemmed Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel
title_short Modeling the non-integer dynamics of a vector-borne infection with nonlocal and nonsingular kernel
title_sort modeling the non integer dynamics of a vector borne infection with nonlocal and nonsingular kernel
topic Fractional calculus
Vector-borne infection
Mathematical model
Existence theory
Fixed-point theorem
Numerical analysis
url https://doi.org/10.1038/s41598-025-90182-1
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