Dynamics of a fractional optimal control HBV infection model with capsids and CTL immune response

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dc.citation.epage244
dc.citation.issue1
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage239
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationРегіональний центр освіти і підвищення кваліфікацій (CRMEF)
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.affiliationCentre R´egional des M´etiers de l’Education et de la Formation (CRMEF)
dc.contributor.authorАіт Ічоу, М.
dc.contributor.authorБахрауі, М.
dc.contributor.authorХаттаф, К.
dc.contributor.authorЮсфі, Н.
dc.contributor.authorAit Ichou, M.
dc.contributor.authorBachraoui, M.
dc.contributor.authorHattaf, K.
dc.contributor.authorYousfi, N.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:54:51Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractУ цій статті розглядається дробова модель оптимального керування, яка описує взаємодію між вірусом гепатиту B (HBV) та капсидами, що містять ДНК HBV, клітинами печінки (гепатоцитами) та імунною відповіддю цитотоксичних Т-клітин. Оптимальне керування виявляє ефективність медикаментозної терапії в інгібуванні виробництва вірусів і запобіганні новим інфекціям. Система оптимальності виведена та розв’язана чисельно. Отримані результати також показують, що оптимальні стратегії лікування зменшують вірусне навантаження та збільшують кількість неінфікованих клітин, що покращує якість життя пацієнта.
dc.description.abstractThis paper deals with a fractional optimal control problem model that describes the interactions between hepatitis B virus (HBV) with HBV DNA-containing capsids, liver cells (hepatocytes), and the cytotoxic T-cell immune response. Optimal controls represent the effectiveness of drug therapy in inhibiting viral production and preventing new infections. The optimality system is derived and solved numerically. Our results also show that optimal treatment strategies reduce viral load and increase the number of uninfected cells, which improves the patient’s quality of life.
dc.format.extent239-244
dc.format.pages6
dc.identifier.citationDynamics of a fractional optimal control HBV infection model with capsids and CTL immune response / M. Ait Ichou, M. Bachraoui, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 239–244.
dc.identifier.citationenDynamics of a fractional optimal control HBV infection model with capsids and CTL immune response / M. Ait Ichou, M. Bachraoui, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 239–244.
dc.identifier.doi10.23939/mmc2023.01.239
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63494
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 1 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 1 (10), 2023
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dc.relation.references[16] Bachraoui M., Hattaf K., Yousfi N. Dynamics of a fractional order HBV infection model with capsids and CTL immune response. Communications in Mathematical Biology and Neuroscience. 2019, 6 (2019).
dc.relation.references[17] Manna K., Chakrabarty S. P. Chronic hepatitis B infection and HBV DNA-containing capsids: Modeling and analysis. Communications in Nonlinear Science and Numerical Simulation. 22 (1–2), 383–395 (2015).
dc.relation.references[18] Manna K. Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response. International Journal of Applied and Computational Mathematics. 3 (3), 2323–2338 (2017).
dc.relation.references[19] Zhou X., Sun Q. Stability analysis of a fractional-order HBV infection model. International Journal of Advances in Applied Mathematics and Mechanics. 2 (2), 1–6 (2014).
dc.relation.references[20] Salman S. M., Yousef A. M. On a fractional-order model for HBV infection with cure of infected cells. Journal of the Egyptian Mathematical Society. 25 (4), 445–451 (2017).
dc.relation.references[21] Cardoso L. C., Dos Santos F. L. P., Camargo R. F. Analysis of fractional-order models for hepatitis B. Computational and Applied Mathematics. 37 (4), 4570–4586 (2018).
dc.relation.references[22] Hattaf K., Yousfi N. A class of delayed viral infection models with general incidence rate and adaptive immune response. International Journal of Dynamics and Control. 4, 254–265 (2016).
dc.relation.references[23] Beddington J. R. Mutual interference between parasites or predators and its effect on searching efficiency. Journal of Animal Ecology. 44 (1), 331–340 (1975).
dc.relation.references[24] DeAngelis D. L., Goldstein A. H., O’Neill R. V. A model for trophic interaction. Ecology. 56, 881–892 (1975).
dc.relation.references[25] Kheiri K., Jafari M. Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing. Journal of Applied Mathematics and Computing. 60, 387–411 (2019).
dc.relation.references[26] Sun H. G., Chen W., Wei H., Chen Y. Q. A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems. The European Physical Journal Special Topics. 193 (1), 185–192 (2011).
dc.relation.referencesen[1] Nowak M. A., Bonhoeffer S., Hill A. M., Boehme R., Thomas H. C., McDade H. Viral dynamics in hepatitis B infection. Proceedings of the National Academy of Sciences of USA. 93 (9), 4398–4402 (1996).
dc.relation.referencesen[2] Ribeiro R. M., Lo A., Perelson A. S. Dynamics of hepatitis B virus infection. Microbes and Infection. 4 (8), 829–835 (2002).
dc.relation.referencesen[3] Hattaf K., Rachik M., Saadi S., Yousfi N. Optimal control of treatment in a basic virus infection model. Applied Mathematical Sciences. 3, 949–958 (2009).
dc.relation.referencesen[4] Elaiw A. M., Alghamdi M. A., Aly S. Hepatitis B virus dynamics: modeling, analysis, and optimal treatment scheduling. Discrete Dynamics in Nature and Society. 2013, 712829 (2013).
dc.relation.referencesen[5] Allali K., Meskaf A., Tridane A. Mathematical modeling of the adaptive immune responses in the early stage of the HBV infection. International Journal of Differential Equations. 2018, 6710575 (2018).
dc.relation.referencesen[6] Mouofo P. T., Tewa J. J., Mewoli B., Bowong S. Optimal control of a delayed system subject to mixed control-state constraints with application to a within-host model of hepatitis virus B. Annual Reviews in Control. 37 (2), 246–259 (2013).
dc.relation.referencesen[7] Sheikhan M., Ghoreishi S. A. Antiviral therapy using a fuzzy controller optimized by modified evolutionary algorithms: a comparative study. Neural Computing and Applications. 23, 1801–1813 (2013).
dc.relation.referencesen[8] Magin R. L. Fractional calculus models of complex dynamics in biological tissues. Computers & Mathematics with Applications. 59 (5), 1586–1593 (2010).
dc.relation.referencesen[9] Saeedian M., Khaliqi M., Azimi–Tafreshi N., Jafari G. R., Ausloos M. Memory effects on epidemic evolution: The susceptible–infected–recovered epidemic model. Physical Review E. 95 (2), 022409 (2017).
dc.relation.referencesen[10] Stanislavsky A. Memory effects and macroscopic manifestation of randomness. Physical Review E. 61 (5), 4752–4759 (2000).
dc.relation.referencesen[11] Pawar D. D., Patil W. D., Raut D. K. Fractional-order mathematical model for analysing impact of quarantine on transmission of COVID-19 in India. Mathematical Modeling and Computing. 8 (2), 253–266 (2021).
dc.relation.referencesen[12] Fadugba S. E., Ali F., Abubakar A. B. Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order. Mathematical Modeling and Computing. 8 (3), 537–548 (2021).
dc.relation.referencesen[13] Khajji B., Boujallal L., Elhia M., Balatif O., Rachik M. A fractional-order model for drinking alcohol behaviour leading to road accidents and violence. Mathematical Modeling and Computing. 9 (3), 501–518 (2022).
dc.relation.referencesen[14] 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[15] Ilnytskyi J. M. Modeling of the COVID-19 pandemic in the limit of no acquired immunity. Mathematical Modeling and Computing. 8 (2), 282–303 (2021).
dc.relation.referencesen[16] Bachraoui M., Hattaf K., Yousfi N. Dynamics of a fractional order HBV infection model with capsids and CTL immune response. Communications in Mathematical Biology and Neuroscience. 2019, 6 (2019).
dc.relation.referencesen[17] Manna K., Chakrabarty S. P. Chronic hepatitis B infection and HBV DNA-containing capsids: Modeling and analysis. Communications in Nonlinear Science and Numerical Simulation. 22 (1–2), 383–395 (2015).
dc.relation.referencesen[18] Manna K. Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response. International Journal of Applied and Computational Mathematics. 3 (3), 2323–2338 (2017).
dc.relation.referencesen[19] Zhou X., Sun Q. Stability analysis of a fractional-order HBV infection model. International Journal of Advances in Applied Mathematics and Mechanics. 2 (2), 1–6 (2014).
dc.relation.referencesen[20] Salman S. M., Yousef A. M. On a fractional-order model for HBV infection with cure of infected cells. Journal of the Egyptian Mathematical Society. 25 (4), 445–451 (2017).
dc.relation.referencesen[21] Cardoso L. C., Dos Santos F. L. P., Camargo R. F. Analysis of fractional-order models for hepatitis B. Computational and Applied Mathematics. 37 (4), 4570–4586 (2018).
dc.relation.referencesen[22] Hattaf K., Yousfi N. A class of delayed viral infection models with general incidence rate and adaptive immune response. International Journal of Dynamics and Control. 4, 254–265 (2016).
dc.relation.referencesen[23] Beddington J. R. Mutual interference between parasites or predators and its effect on searching efficiency. Journal of Animal Ecology. 44 (1), 331–340 (1975).
dc.relation.referencesen[24] DeAngelis D. L., Goldstein A. H., O’Neill R. V. A model for trophic interaction. Ecology. 56, 881–892 (1975).
dc.relation.referencesen[25] Kheiri K., Jafari M. Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing. Journal of Applied Mathematics and Computing. 60, 387–411 (2019).
dc.relation.referencesen[26] Sun H. G., Chen W., Wei H., Chen Y. Q. A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems. The European Physical Journal Special Topics. 193 (1), 185–192 (2011).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectдробова похідна
dc.subjectHBV-інфекція
dc.subjectоптимальне керування
dc.subjectCTLреакція
dc.subjectчисельне моделювання
dc.subjectfractional derivative
dc.subjectHBV infection
dc.subjectoptimal control
dc.subjectCTL response
dc.subjectnumerical simulations
dc.titleDynamics of a fractional optimal control HBV infection model with capsids and CTL immune response
dc.title.alternativeДинаміка дробової моделі оптимального керування HBV-інфекцією з капсидами та імунною відповіддю CTL
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 1