Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator
| dc.citation.epage | 332 | |
| dc.citation.issue | 11 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 319 | |
| dc.citation.volume | 1 | |
| dc.contributor.affiliation | Університет Хасана ІІ Касабланки | |
| dc.contributor.affiliation | Регіональний центр освіти і підготовки професій (CRMEF) | |
| dc.contributor.affiliation | Hassan II University of Casablanca | |
| dc.contributor.affiliation | Centre R´egional des M´etiers de l’Education et de la Formation (CRMEF) | |
| dc.contributor.author | Ель Хассані, А. | |
| dc.contributor.author | Беттіуї, Б. | |
| dc.contributor.author | Хаттаф, К. | |
| dc.contributor.author | Ахтаїч, Н. | |
| dc.contributor.author | El Hassani, A. | |
| dc.contributor.author | Bettioui, B. | |
| dc.contributor.author | Hattaf, K. | |
| dc.contributor.author | Achtaich, N. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-10-20T07:44:22Z | |
| dc.date.created | 2024-02-24 | |
| dc.date.issued | 2024-02-24 | |
| dc.description.abstract | У цій статті пропонується та досліджується глобальна динаміка моделі інфекції SARS-CoV-2 з дифузією та противірусним лікуванням. Запропонована модель враховує два способи передачі (від вірусу до клітини та від клітини до клітини), літичну та нелітичну імунні відповіді. Дифузія в модель формулюється за допомогою регіонального дробового оператора Лапласа. Крім того, глобальна асимптотична стійкість рівноваг суворо встановлюється за допомогою нового запропонованого методу побудови функцій Ляпунова для класу диференціальних рівнянь з частинними похідними (ДРП) з регіональним дробовим оператором Лапласа. Запропонований метод застосовується до класичних рівнянь реакції-дифузії з нормальною дифузією. | |
| dc.description.abstract | In this paper, we propose and investigate the global dynamics of a SARS-CoV-2 infection model with diffusion and antiviral treatment. The proposed model takes into account the two modes of transmission (virus-to-cell and cell-to-cell), the lytic and nonlytic immune responses. The diffusion into the model is formulated by the regional fractional Laplacian operator. Furthermore, the global asymptotic stability of equilibria is rigorously established by means of a new proposed method constructing Lyapunov functions for a class of partial differential equations (PDEs) with regional fractional Laplacian operator. The proposed method is applied to the classical reaction-diffusion equations with normal diffusion. | |
| dc.format.extent | 319-332 | |
| dc.format.pages | 14 | |
| dc.identifier.citation | Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator / A. El Hassani, B. Bettioui, K. Hattaf, N. Achtaich // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 319–332. | |
| dc.identifier.citationen | Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator / A. El Hassani, B. Bettioui, K. Hattaf, N. Achtaich // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 319–332. | |
| dc.identifier.doi | 10.23939/mmc2024.01.319 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/113791 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 11 (1), 2024 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 11 (1), 2024 | |
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| dc.relation.references | [12] Zhang L., Sun J. W. Global stability of a nonlocal epidemic model with delay. Taiwanese Journal of Mathematics. 20 (3), 577–587 (2016). | |
| dc.relation.references | [13] Elaiw A., Al Agha A. Global analysis of a reaction-diffusion with in-host Malaria infection model with adaptive immune response. Mathematics. 8 (4), 563 (2020). | |
| dc.relation.references | [14] Hattaf K., Yousfi N. Global stability for fractional diffusion equations in biological systems. Complexity. 2020, 5476842 (2020). | |
| dc.relation.references | [15] El Hassani A., Hattaf K., Achtaich N. Global stability of reaction-diffusion equations with fractional Laplacian operator and applications in biology. Communications in Mathematical Biology and Neuroscience. 2022, 56 (2022). | |
| dc.relation.references | [16] Guan Q.-Y. Integration by parts formula for regional fractional Laplacian. Communications in Mathematical Physics. 266, 289–329 (2006). | |
| dc.relation.references | [17] Hattaf K., Yousfi N. Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response. Mathematical Biosciences and Engineering. 17 (5), 5326–5340 (2020). | |
| dc.relation.references | [18] Hattaf K., Yousfi N. Qualitative analysis of a generalized virus dynamics model with both modes of transmission and distributed delays. International Journal of Differential Equations. 2018, 9818372 (2018). | |
| dc.relation.references | [19] Hattaf K., Yousfi N. Modeling the adaptive immunity and both modes of transmission in HIV infection. Computation. 6 (2), 37 (2018). | |
| dc.relation.references | [20] Gal C. G., Warma M. Reaction–diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions. Discrete and Continuous Dynamical Systems. 36 (3), 1279–1319 (2016). | |
| dc.relation.references | [21] Kajiwara T., Sasaki T., Takeuchi Y. Construction of Lyapunov functionals for delay differential equations in virology and epidemiology. Nonlinear Analysis: Real World Applications. 13 (4), 1802–1826 (2012). | |
| dc.relation.references | [22] Huang Y., Oberman A. Numerical methods for the fractional Laplacian: A finite difference-quadrature approach. SIAM Journal on Numerical Analysis. 52 (6), 3056–3084 (2014). | |
| dc.relation.references | [23] Valdinoci E. From the long jump random walk to the fractional Laplacian. Boletin de la Sociedad Espanola de Matematica Aplicada. SeMA. 49, 33–44 (2009). | |
| dc.relation.referencesen | [1] Elaiw A. M., Hobiny A. D., Al Agha A. D. Global dynamics of SARS-CoV-2/cancer model with immune responses. Applied Mathematics and Computation. 408, 126364 (2021). | |
| dc.relation.referencesen | [2] Kevrekidis P. G., Cuevas-Maraver J., Drossinos Y., Rapti Z., Kevrekidis G. A. Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples. Physical Review E. 104 (2), 024412 (2021). | |
| dc.relation.referencesen | [3] Elaiw A. M., Shflot A. S., Hobiny A. D., Aly S. A. Global Dynamics of an HTLV-I and SARS-CoV-2 CoInfection Model with Diffusion. Mathematics. 11 (3), 688 (2023). | |
| dc.relation.referencesen | [4] Bucur C., Valdinoci E. Nonlocal Diffusion and Applications. Lecture Notes of the Unione Matematica Italiana. Springer (2016). | |
| dc.relation.referencesen | [5] Somathilake L. W., Burrage K. A space-fractional-reaction-diffusion model for pattern formation in coral reefs. Cogent Mathematics & Statistics. 5 (1), 1426524 (2018). | |
| dc.relation.referencesen | [6] Nezza E. D., Palatucci G., Valdinoci E. Hitchhiker’s guide to the fractional Sobolev spaces. Bulletin des Sciences Math´ematiques. 136 (5), 521–573 (2012). | |
| dc.relation.referencesen | [7] V´azquez J. L. Nonlinear Diffusion with Fractional Laplacian Operators. Nonlinear partial differential equations. 271–298 (2012). | |
| dc.relation.referencesen | [8] Bogdan K., Burdzy K., Chen Z.-Q. Censored stable processes. Probabity Theory Related Fields. 127, 89–152 (2003). | |
| dc.relation.referencesen | [9] Duo S., Wang H., Zhang Y. A comparative study on nonlocal diffusion operators related to the fractional Laplacian. Discrete and Continuous Dynamical Systems - B. 24 (1), 231–256 (2019). | |
| dc.relation.referencesen | [10] Hattaf K., Yousfi N. Global stability for reaction-diffusion equations in biology. Computers & Mathematics with Applications. 66 (8), 1488–1497 (2013). | |
| dc.relation.referencesen | [11] Zhang T., Zhang T., Meng X. Stability analysis of a chemostat model with maintenance energy. Applied Mathematics Letters. 68, 1–7 (2017). | |
| dc.relation.referencesen | [12] Zhang L., Sun J. W. Global stability of a nonlocal epidemic model with delay. Taiwanese Journal of Mathematics. 20 (3), 577–587 (2016). | |
| dc.relation.referencesen | [13] Elaiw A., Al Agha A. Global analysis of a reaction-diffusion with in-host Malaria infection model with adaptive immune response. Mathematics. 8 (4), 563 (2020). | |
| dc.relation.referencesen | [14] Hattaf K., Yousfi N. Global stability for fractional diffusion equations in biological systems. Complexity. 2020, 5476842 (2020). | |
| dc.relation.referencesen | [15] El Hassani A., Hattaf K., Achtaich N. Global stability of reaction-diffusion equations with fractional Laplacian operator and applications in biology. Communications in Mathematical Biology and Neuroscience. 2022, 56 (2022). | |
| dc.relation.referencesen | [16] Guan Q.-Y. Integration by parts formula for regional fractional Laplacian. Communications in Mathematical Physics. 266, 289–329 (2006). | |
| dc.relation.referencesen | [17] Hattaf K., Yousfi N. Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response. Mathematical Biosciences and Engineering. 17 (5), 5326–5340 (2020). | |
| dc.relation.referencesen | [18] Hattaf K., Yousfi N. Qualitative analysis of a generalized virus dynamics model with both modes of transmission and distributed delays. International Journal of Differential Equations. 2018, 9818372 (2018). | |
| dc.relation.referencesen | [19] Hattaf K., Yousfi N. Modeling the adaptive immunity and both modes of transmission in HIV infection. Computation. 6 (2), 37 (2018). | |
| dc.relation.referencesen | [20] Gal C. G., Warma M. Reaction–diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions. Discrete and Continuous Dynamical Systems. 36 (3), 1279–1319 (2016). | |
| dc.relation.referencesen | [21] Kajiwara T., Sasaki T., Takeuchi Y. Construction of Lyapunov functionals for delay differential equations in virology and epidemiology. Nonlinear Analysis: Real World Applications. 13 (4), 1802–1826 (2012). | |
| dc.relation.referencesen | [22] Huang Y., Oberman A. Numerical methods for the fractional Laplacian: A finite difference-quadrature approach. SIAM Journal on Numerical Analysis. 52 (6), 3056–3084 (2014). | |
| dc.relation.referencesen | [23] Valdinoci E. From the long jump random walk to the fractional Laplacian. Boletin de la Sociedad Espanola de Matematica Aplicada. SeMA. 49, 33–44 (2009). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2024 | |
| dc.subject | SARS-CoV-2 | |
| dc.subject | COVID-19 | |
| dc.subject | регіональний дробовий оператор Лапласа | |
| dc.subject | дифузія | |
| dc.subject | функції Ляпунова | |
| dc.subject | глобальна стійкість | |
| dc.subject | SARS-CoV-2 | |
| dc.subject | COVID-19 | |
| dc.subject | regional fractional Laplacian operator | |
| dc.subject | diffusion | |
| dc.subject | Lyapunov functions | |
| dc.subject | global stability | |
| dc.title | Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator | |
| dc.title.alternative | Глобальна динаміка дифузійної моделі SARS-CoV-2 з противірусним лікуванням і дробовим оператором Лапласа | |
| dc.type | Article |
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