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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Nature Portfolio
2025-02-01
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| 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. |
| format | Article |
| id | doaj-art-b4cd7160c5414801a3af1ebec00db1c3 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| 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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