A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account

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dc.citation.epage65
dc.citation.issue1
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage53
dc.contributor.affiliationЛабораторія аналізу, моделювання та симуляції, Касабланка
dc.contributor.affiliationLaboratory of Analysis, Modeling and Simulation of Casablanca
dc.contributor.authorХалуфі, І.
dc.contributor.authorЛафіф, М.
dc.contributor.authorБенфата, Й.
dc.contributor.authorЛаарабі, Х.
dc.contributor.authorБуягрумні, Дж.
dc.contributor.authorРачік, М.
dc.contributor.authorKhaloufi, I.
dc.contributor.authorLafif, M.
dc.contributor.authorBenfatah, Y.
dc.contributor.authorLaarabi, H.
dc.contributor.authorBouyaghroumni, J.
dc.contributor.authorRachik, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:54:53Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractУ цій статті пропонується математична модель зараження інфекційними захворюваннями, яка враховує стратифікацію населення на основі критеріїв імунітету. Метою є продемонструвати ефективність цієї ідеї в запобіганні різним епідеміям і зменшити значні фінансові та людські витрати, які спричиняють ці захворювання. Визначено фундаментальну швидкість відтворення і за допомогою цієї швидкості перевірено стійкість вільної точки рівноваги, а потім запропоновано дві міри керування. Для опису оптимальних керувань використано принцип максимуму Понтрягіна, а для розв’язування системи керування — ітераційний підхід. Накінець, чисельне моделювання виконується в MATLAB для перевірки теоретичного аналізу.
dc.description.abstractA mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed. Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause. We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures. The Pontryagin’s maximum principle is used to describe the optimal controls, and an iterative approach is used to solve the optimality system. Finally, numerical simulations are carried out in MATLAB to verify the theoretical analysis.
dc.format.extent53-65
dc.format.pages13
dc.identifier.citationA continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account / I. Khaloufi, M. Lafif, Y. Benfatah, H. Laarabi, J. Bouyaghroumni, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 53–65.
dc.identifier.citationenA continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account / I. Khaloufi, M. Lafif, Y. Benfatah, H. Laarabi, J. Bouyaghroumni, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 53–65.
dc.identifier.doidoi.org/10.23939/mmc2023.01.053
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63500
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
dc.relation.references[1] Delves P. J., Roitt I. M. The immune system. New England Journal of Medicine. 343 (1), 37–49 (2000).
dc.relation.references[2] Pancer Z., Cooper M. D. The evolution of adaptive immunity. Annual Review of Immunology. 24 (1), 497–518 (2006).
dc.relation.references[3] Hoebe K., Janssen E., Beutler B. The interface between innate and adaptive immunity. Nature Immunology. 5 (10), 971–974 (2004).
dc.relation.references[4] Mitchison N. A. The carrier effect in the secondary response to hapten-protein conjugates. II. Cellular cooperation. European journal of immunology. 1 (1), 18–27 (1971).
dc.relation.references[5] Stewart-Tull D. E. The Theory and Practical Application of Adjuvants. Wiley (1995).
dc.relation.references[6] Thompson K., Harris M., Benjamini E., Mitchell G., Noble M. Cellular and humoral immunity: a distinction in antigenic recognition. Nature New Biology. 238 (79), 20–21 (1972).
dc.relation.references[7] Cantor H., Boyse E. A. Regulation of cellular and humoral immune responses by T-cell subclasses. In: Cold Spring Harbor symposia on quantitative biology. 41, 23–32. Cold Spring Harbor Laboratory Press (1977).
dc.relation.references[8] Novotn´y J., Bruccoleri R., Newell J., Murphy D., Haber E., Karplus M. Molecular anatomy of the antibody binding site. Journal of Biological Chemistry. 258 (23), 14433–14437 (1983).
dc.relation.references[9] Garcia K. C., Teyton L., Wilson I. A. Structural basis of T cell recognition. Annual Review of Immunology. 17, 369–397 (1999).
dc.relation.references[10] Turvey S. E., Broide D. H. Innate immunity. Journal of Allergy and Clinical Immunology. 125 (2), S24–S32 (2010).
dc.relation.references[11] Nevard C., Gaunt M., Ockleford C. The Transfer of Passive and Active Immunity. In: The Immunology of the Fetus. 193–214. CRC Press (2020).
dc.relation.references[12] Rich R. R., Chaplin D. D. The Human Immune Response. In: Clinical Immunology (Fifth Edition). 3–17. Elsevier (2019).
dc.relation.references[13] Freeman G. J., Casasnovas J. M., Umetsu D. T., DeKruyff R. H. TIM genes: a family of cell surface phosphatidylserine receptors that regulate innate and adaptive immunity. Immunological Reviews. 235 (1), 172–189 (2010).
dc.relation.references[14] Bell J. I., Todd J. A., McDevitt H. O. The Molecular Basis of HLA–Disease Association. In: Harris H., Hirschhorn K. (eds) Advances in Human Genetics. 18, 1–41 (1989).
dc.relation.references[15] Evans A. S. Viral Infections of Humans: Epidemiology and Control. Springer Science & Business Media (2013).
dc.relation.references[16] Burrell C. J., Howard C. R., Murphy F. A. Pathogenesis of Virus Infections. Fenner and White’s Medical Virology (Fifth Edition). 77–104 (2017).
dc.relation.references[17] Duggal S., Chugh T. D., Duggal A. K. HIV and malnutrition: effects on immune system. Journal of Immunology Research. 2012, 784740 (2012).
dc.relation.references[18] Perelson A. S. Modeling the interaction of the immune system with HIV. In: Castillo-Chavez C. (eds) Mathematical and Statistical Approaches to AIDS Epidemiology. 83, 350–370 (1989).
dc.relation.references[19] Volberding P. A., Deeks S. G. Antiretroviral therapy and management of HIV infection. The Lancet. 376 (9734), 49–62 (2010).
dc.relation.references[20] Lekka M. Discrimination between normal and cancerous cells using AFM. BioNanoScience. 6 (1), 65–80 (2016).
dc.relation.references[21] Armstrong A. C., Eaton D., Ewing J. C. Cellular immunotherapy for cancer. BMJ. 323 (7324), 1289–1293 (2001).
dc.relation.references[22] Lafif M., Khaloufi I., Benfatah Y., Bouyaghroumni J., Laarabi H., Rachik M. A mathematical SIR model on the spread of infectious diseases considering human immunity. Communications in Mathematical Biology and Neuroscience. 2022, 69 (2022).
dc.relation.references[23] El Bhih A., Benfatah Y., Ghazaoui A., Rachik M. On the maximal output set of fractional-order discrete-time linear systems. Mathematical Modeling and Computing. 9 (2), 262–277 (2022).
dc.relation.references[24] El Bhih A., Benfatah Y., Ben Rhila S., Rachik M., El Alami Laaroussi A. A spatiotemporal prey-predator discrete model and optimal controls for environmental sustainability in the multifishing areas of Morocco. Discrete Dynamics in Nature and Society. 2020, 2780651 (2020).
dc.relation.references[25] Perko L. Differential Equations and Dynamical Systems. Springer (2014).
dc.relation.references[26] Bani-Yaghoub M., Gautam R., Shuai Z., Van Den Driessche P., Ivanek R. Reproduction numbers for infections with free-living pathogens growing in the environment. Journal of biological dynamics. 6 (2), 923–940 (2012).
dc.relation.references[27] Fleming W. H., Rishel R. W. Deterministic and Stochastic Optimal Control. 1. Springer Science & Business Media (2012).
dc.relation.references[28] Kouidere A., Kada D., Balatif O., Rachik M., Naim M. Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness. Chaos, Solitons & Fractals. 142, 110438 (2021).
dc.relation.references[29] Pontryagin L. S. Mathematical Theory of Optimal Processes. CRC press (1987).
dc.relation.references[30] Benfatah Y., Khaloufi I., Boutayeb H., Rachik M., Laarabi H. Optimal control for a discrete time epidemic model with zones evolution. Communications in Mathematical Biology and Neuroscience. 2022, 51 (2022).
dc.relation.references[31] Khaloufi I., Benfatah Y., Laarabi H., Rachik M. A scenario to fight monkeypox using a mathematical model. Communications in Mathematical Biology and Neuroscience. 2022, 99 (2022).
dc.relation.referencesen[1] Delves P. J., Roitt I. M. The immune system. New England Journal of Medicine. 343 (1), 37–49 (2000).
dc.relation.referencesen[2] Pancer Z., Cooper M. D. The evolution of adaptive immunity. Annual Review of Immunology. 24 (1), 497–518 (2006).
dc.relation.referencesen[3] Hoebe K., Janssen E., Beutler B. The interface between innate and adaptive immunity. Nature Immunology. 5 (10), 971–974 (2004).
dc.relation.referencesen[4] Mitchison N. A. The carrier effect in the secondary response to hapten-protein conjugates. II. Cellular cooperation. European journal of immunology. 1 (1), 18–27 (1971).
dc.relation.referencesen[5] Stewart-Tull D. E. The Theory and Practical Application of Adjuvants. Wiley (1995).
dc.relation.referencesen[6] Thompson K., Harris M., Benjamini E., Mitchell G., Noble M. Cellular and humoral immunity: a distinction in antigenic recognition. Nature New Biology. 238 (79), 20–21 (1972).
dc.relation.referencesen[7] Cantor H., Boyse E. A. Regulation of cellular and humoral immune responses by T-cell subclasses. In: Cold Spring Harbor symposia on quantitative biology. 41, 23–32. Cold Spring Harbor Laboratory Press (1977).
dc.relation.referencesen[8] Novotn´y J., Bruccoleri R., Newell J., Murphy D., Haber E., Karplus M. Molecular anatomy of the antibody binding site. Journal of Biological Chemistry. 258 (23), 14433–14437 (1983).
dc.relation.referencesen[9] Garcia K. C., Teyton L., Wilson I. A. Structural basis of T cell recognition. Annual Review of Immunology. 17, 369–397 (1999).
dc.relation.referencesen[10] Turvey S. E., Broide D. H. Innate immunity. Journal of Allergy and Clinical Immunology. 125 (2), S24–S32 (2010).
dc.relation.referencesen[11] Nevard C., Gaunt M., Ockleford C. The Transfer of Passive and Active Immunity. In: The Immunology of the Fetus. 193–214. CRC Press (2020).
dc.relation.referencesen[12] Rich R. R., Chaplin D. D. The Human Immune Response. In: Clinical Immunology (Fifth Edition). 3–17. Elsevier (2019).
dc.relation.referencesen[13] Freeman G. J., Casasnovas J. M., Umetsu D. T., DeKruyff R. H. TIM genes: a family of cell surface phosphatidylserine receptors that regulate innate and adaptive immunity. Immunological Reviews. 235 (1), 172–189 (2010).
dc.relation.referencesen[14] Bell J. I., Todd J. A., McDevitt H. O. The Molecular Basis of HLA–Disease Association. In: Harris H., Hirschhorn K. (eds) Advances in Human Genetics. 18, 1–41 (1989).
dc.relation.referencesen[15] Evans A. S. Viral Infections of Humans: Epidemiology and Control. Springer Science & Business Media (2013).
dc.relation.referencesen[16] Burrell C. J., Howard C. R., Murphy F. A. Pathogenesis of Virus Infections. Fenner and White’s Medical Virology (Fifth Edition). 77–104 (2017).
dc.relation.referencesen[17] Duggal S., Chugh T. D., Duggal A. K. HIV and malnutrition: effects on immune system. Journal of Immunology Research. 2012, 784740 (2012).
dc.relation.referencesen[18] Perelson A. S. Modeling the interaction of the immune system with HIV. In: Castillo-Chavez C. (eds) Mathematical and Statistical Approaches to AIDS Epidemiology. 83, 350–370 (1989).
dc.relation.referencesen[19] Volberding P. A., Deeks S. G. Antiretroviral therapy and management of HIV infection. The Lancet. 376 (9734), 49–62 (2010).
dc.relation.referencesen[20] Lekka M. Discrimination between normal and cancerous cells using AFM. BioNanoScience. 6 (1), 65–80 (2016).
dc.relation.referencesen[21] Armstrong A. C., Eaton D., Ewing J. C. Cellular immunotherapy for cancer. BMJ. 323 (7324), 1289–1293 (2001).
dc.relation.referencesen[22] Lafif M., Khaloufi I., Benfatah Y., Bouyaghroumni J., Laarabi H., Rachik M. A mathematical SIR model on the spread of infectious diseases considering human immunity. Communications in Mathematical Biology and Neuroscience. 2022, 69 (2022).
dc.relation.referencesen[23] El Bhih A., Benfatah Y., Ghazaoui A., Rachik M. On the maximal output set of fractional-order discrete-time linear systems. Mathematical Modeling and Computing. 9 (2), 262–277 (2022).
dc.relation.referencesen[24] El Bhih A., Benfatah Y., Ben Rhila S., Rachik M., El Alami Laaroussi A. A spatiotemporal prey-predator discrete model and optimal controls for environmental sustainability in the multifishing areas of Morocco. Discrete Dynamics in Nature and Society. 2020, 2780651 (2020).
dc.relation.referencesen[25] Perko L. Differential Equations and Dynamical Systems. Springer (2014).
dc.relation.referencesen[26] Bani-Yaghoub M., Gautam R., Shuai Z., Van Den Driessche P., Ivanek R. Reproduction numbers for infections with free-living pathogens growing in the environment. Journal of biological dynamics. 6 (2), 923–940 (2012).
dc.relation.referencesen[27] Fleming W. H., Rishel R. W. Deterministic and Stochastic Optimal Control. 1. Springer Science & Business Media (2012).
dc.relation.referencesen[28] Kouidere A., Kada D., Balatif O., Rachik M., Naim M. Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness. Chaos, Solitons & Fractals. 142, 110438 (2021).
dc.relation.referencesen[29] Pontryagin L. S. Mathematical Theory of Optimal Processes. CRC press (1987).
dc.relation.referencesen[30] Benfatah Y., Khaloufi I., Boutayeb H., Rachik M., Laarabi H. Optimal control for a discrete time epidemic model with zones evolution. Communications in Mathematical Biology and Neuroscience. 2022, 51 (2022).
dc.relation.referencesen[31] Khaloufi I., Benfatah Y., Laarabi H., Rachik M. A scenario to fight monkeypox using a mathematical model. Communications in Mathematical Biology and Neuroscience. 2022, 99 (2022).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectдинамічна система
dc.subjectімунітет людини
dc.subjectінфекційні хвороби
dc.subjectстійкість
dc.subjectвільна рівновага
dc.subjectоптимальне керування
dc.subjectdynamic system
dc.subjecthuman immunity
dc.subjectinfectious diseases
dc.subjectstability
dc.subjectfree equilibrium
dc.subjectoptimal control
dc.titleA continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account
dc.title.alternativeНеперервна математична модель SIR поширення інфекційних хвороб з урахуванням імунітету людини
dc.typeArticle

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