Viral infection model with cell-to-cell transmission and therapy in the presence of humoral immunity: Global analysis

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dc.citation.epage1050
dc.citation.issue4
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage1037
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationУніверситет Хасана І
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.affiliationHassan First University
dc.contributor.authorЕль Акраа, Н.
dc.contributor.authorЛахбі, М.
dc.contributor.authorДанане, Дж.
dc.contributor.authorEl Akraa, N.
dc.contributor.authorLahby, M.
dc.contributor.authorDanane, J.
dc.coverage.placenameЛьвів
dc.date.accessioned2025-03-10T09:22:02Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractЦя стаття спрямована на моделювання математичної моделі вірусної інфекції, яка включає як безклітинну передачу, так і міжклітинну передачу. Модель включає чотири відділи, а саме: чутливі, інфіковані, вірусне навантаження та гуморальну імунну відповідь, яка активується в господаря для атаки на вірус. Спершу встановлено коректність запропонованої математичної моделі з точки зору доведення існування, додатності та обмеженості розв’язків. Крім того, визначено різні рівноваги задачі. Також досліджено глобальну стійкість кожної рівноваги. Накінець, проведено чисельне моделювання, щоб підтвердити теоретичні висновки та дослідити ефект різних типів лікування, які пропонуються в моделі.
dc.description.abstractThis paper aims to prezent mathematical model for Viral infection which incorporates both the cell-free and cell-to-cell transmission. The model includes four compartments, namely, the susceptible, the infected ones, the viral load and the humoral immune response, which is activated in the host to attack the virus. Firstly, we establish the well-posedness of our mathematical model in terms of proving the existence, positivity and boundedness of solutions. Moreover, we determine the different equilibrium of the problem. Also, we will study the global stability of each equilibrium. Finally, we give some numerical simulation in order to validate our theoretical findings, and to study the effect of different types of treatments proposed by the model.
dc.format.extent1037-1050
dc.format.pages14
dc.identifier.citationEl Akraa N. Viral infection model with cell-to-cell transmission and therapy in the presence of humoral immunity: Global analysis / N. El Akraa, M. Lahby, J. Danane // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1037–1050.
dc.identifier.citationenEl Akraa N. Viral infection model with cell-to-cell transmission and therapy in the presence of humoral immunity: Global analysis / N. El Akraa, M. Lahby, J. Danane // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1037–1050.
dc.identifier.doidoi.org/10.23939/mmc2023.04.1037
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/64085
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 4 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 4 (10), 2023
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dc.relation.referencesen[1] Burchell A. N., Winer R. L., de Sanjos´e S., Franco E. L. Epidemiology and transmission dynamics of genital HPV infection. Vaccine. 24 (Suppl. 3), S52–S61 (2006).
dc.relation.referencesen[2] Elbasha E. H., Dasbach E. J., Insinga R. P. A multi-type HPV transmission model. Bulletin of Mathematical Biology. 70 (8), 2126–2176 (2008).
dc.relation.referencesen[3] Perelson A. S., Neumann A. U., Markowitz M., Leonard J. M., Ho D. D. HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science. 271 (5255), 1582–1586 (1996).
dc.relation.referencesen[4] Adams B. M., Banks H. T., Davidian M., Kwon H.-D., Tran H. T., Wynne S. N., Rosenberg E. S. HIV dynamics: modeling, data analysis, and optimal treatment protocols. Journal of Computational and Applied Mathematics. 184 (1), 10–49 (2005).
dc.relation.referencesen[5] Wodarz D. Hepatitis C virus dynamics and pathology: the role of CTL and antibody responses. Journal of General Virology. 84 (7), 1743–1750 (2003).
dc.relation.referencesen[6] Sadki M., Danane J., Allali K. Hepatitis C virus fractional-order model: mathematical analysis. Modeling Earth Systems and Environment. 9, 1695–1707 (2023).
dc.relation.referencesen[7] Danane J., Allali K., Hammouch Z. Mathematical analysis of a fractional differential model of HBV infection with antibody immune response. Chaos, Solitons & Fractals. 136, 109787 (2020).
dc.relation.referencesen[8] Li M., Zu J. The review of differential equation models of HBV infection dynamics. Journal of Virological Methods. 266, 103–113 (2019).
dc.relation.referencesen[9] Estrada E. COVID-19 and SARS-CoV-2. Modeling the present, looking at the future. Physics Reports. 869, 1–51 (2020).
dc.relation.referencesen[10] Danane J., Hammouch Z., Allali K., Rashid S., Singh J. A fractional-order model of coronavirus disease 2019 (COVID-19) with governmental action and individual reaction. Mathematical Methods in the Applied Sciences. 46 (7), 8275–8288 (2023).
dc.relation.referencesen[11] U¸car E., Ozdemir N., Altun E. Qualitative analysis and numerical simulations of new model describing ¨cancer. Journal of Computational and Applied Mathematics. 422, 114899 (2023).
dc.relation.referencesen[12] Nowak M. A., Bangham C. R. M. Population dynamics of immune responses to persistent viruses. Science. 272 (5258), 74–79 (1996).
dc.relation.referencesen[13] Dunia R., Bonnecaze R. Mathematical modeling of viral infection dynamics in spherical organs. Journal of Mathematical Biology. 67 (6), 1425–1455 (2013).
dc.relation.referencesen[14] Neumann A. U., Lam N. P., Dahari H., Gretch D. R., Wiley T. E., Layden T. J., Perelson A. S. Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-α therapy. Science. 282 (5386), 103–107 (1998).
dc.relation.referencesen[15] Brimacombe C. L., Grove J., Meredith L. W., Hu K., Syder A. J., Flores M. V., Timpe J. M., Krieger S. E., Baumert T. F., Tellinghuisen T. L., Wong-Staal F., Balfe P., McKeating J. A. Neutralizing antibodyresistant hepatitis C virus cell-to-cell transmission. Journal of Virology. 85 (1), 596–605 (2011).
dc.relation.referencesen[16] Mojaver A., Kheiri H. Dynamical analysis of a class of hepatitis C virus infection models with application of optimal control. International Journal of Biomathematics. 9 (3), 1650038 (2016).
dc.relation.referencesen[17] Cao X., Roy A. K., Al Basir F., Roy P. K. Global dynamics of HIV infection with two disease transmission routes-a mathematical model. Communications in Mathematical Biology and Neuroscience. 2020, 8 (2020).
dc.relation.referencesen[18] Sadki M., Harroudi S., Allali K. Dynamical analysis of an HCV model with cell-to-cell transmission and cure rate in the presence of adaptive immunity. Mathematical Modeling and Computing. 9 (3), 579–593 (2022).
dc.relation.referencesen[19] Reluga T. C., Dahari H., Perelson A. S. Analysis of hepatitis C virus infection models with hepatocyte homeostasis. SIAM Journal on Applied Mathematics. 69 (4), 999–1023 (2009).
dc.relation.referencesen[20] Alberts B., Johnson A., Lewis J., Raff M., Roberts K., Walter P. Molecular Biology of the Cell. Garland Science, New York (2002).
dc.relation.referencesen[21] Danane J., Allali K. Optimal control of an HIV model with CTL cells and latently infected cells. Numerical Algebra, Control and Optimization. 10 (2), 207–225 (2020).
dc.relation.referencesen[22] Hattaf K., Yousfi N. Two optimal treatments of HIV infection model. World Journal of Modelling and Simulation. 8 (1), 27–35 (2012).
dc.relation.referencesen[23] Van den Driessche P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. 180 (1–2), 29-48 (2002).
dc.relation.referencesen[24] Chen S.-S., Cheng C.-Y., Takeuchi Y. Stability analysis in delayed within-host viral dynamics with both viral and cellular infections. Journal of Mathematical Analysis and Applications. 442 (2), 642–672 (2016).
dc.relation.referencesen[25] Hale J. K., Lunel S. M. V. Introduction to Functional Differential Equations. Applied Mathematical Sciences. Springer, New York (2013).
dc.relation.referencesen[26] Ait Ichou M., Bachraoui M., Hattaf K., Yousfi N. Dynamics of a fractional optimal control HBV infection model with capsids and CTL immune response. Mathematical Modeling and Computing. 10 (1), 239–244 (2023).
dc.relation.referencesen[27] Ghanbari B. A new model for investigating the transmission of infectious diseases in a prey-predator system using a non-singular fractional derivative. Mathematical Methods in the Applied Sciences. 44 (13), 9998–10013 (2021).
dc.relation.referencesen[28] Almeida R., Brito da Cruz A. M. C., Martins N., Monteiro M. T. T. An epidemiological MSEIR model described by the Caputo fractional derivative. International Journal of Dynamics and Control. 7, 776–784 (2019).
dc.relation.referencesen[29] Bounkaicha C., Allali K., Tabit Y., Danane J. Global dynamic of spatio-temporal fractional order SEIR model. Mathematical Modeling and Computing. 10 (2), 299–310 (2023).
dc.relation.referencesen[30] Elkaf M., Allali K. Fractional derivative model for tumor cells and immune system competition. Mathematical Modeling and Computing. 10 (2), 288–298 (2023).
dc.relation.referencesen[31] Kiouach D., Sabbar Y. Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation. International Journal of Biomathematics. 14 (04), 2150016 (2021).
dc.relation.referencesen[32] Rihan F. A., Alsakaji H. J. Analysis of a stochastic HBV infection model with delayed immune response. Mathematical Biosciences and Engineering. 18 (5), 5194–5220 (2021).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectглобальна стійкість
dc.subjectвід клітини до клітини
dc.subjectгуморальна імунна відповідь
dc.subjectтерапія
dc.subjectбазовий номер відтворення
dc.subjectчисельне моделювання
dc.subjectglobal stability
dc.subjectcell-to-cell
dc.subjecthumoral immune response
dc.subjecttherapy
dc.subjectbasic reproduction number
dc.subjectnumerical simulation
dc.titleViral infection model with cell-to-cell transmission and therapy in the presence of humoral immunity: Global analysis
dc.title.alternativeМодель вірусної інфекції з міжклітинною передачею та терапією за наявності гуморального імунітету: глобальний аналіз
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 4