The impact of rumors on the success of Covid-19 vaccination programs in a Coronavirus-infected environment: optimal control approach

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dc.citation.epage263
dc.citation.issue11
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage250
dc.citation.volume1
dc.contributor.affiliationУніверситет Чуайба Дуккалі
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationChouaib Doukkali University, El Jadida
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.authorБалатіф, О.
dc.contributor.authorКуідере, А.
dc.contributor.authorКада, Д.
dc.contributor.authorРачик, М.
dc.contributor.authorBalatif, O.
dc.contributor.authorKouidere, A.
dc.contributor.authorKada, D.
dc.contributor.authorRachik, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T07:44:17Z
dc.date.created2024-02-24
dc.date.issued2024-02-24
dc.description.abstractУ цій статті запропоновано математичну модель, яка описує вплив чуток на успіх програм вакцинації проти Covid-19 у середовищі, зараженому коронавірусом. Метою цього дослідження є висвітлення ролі боротьби з поширенням чуток щодо ризиків вакцинації та ревакцинаційних доз в успіху програм вакцинації та досягненні колективного імунітету. Крім того, ми формулюємо задачу оптимального управління, пропонуючи кілька стратегій, включаючи програми підвищення обізнаності та боротьби з чутками, щоб допомогти посадовцям країни досягти успішних програм вакцинації з оптимальними зусиллями. Досліджується існування оптимальних управлінських засобів, а для їх характеристики використовується принцип максимуму Понтрягіна. Система оптимальності розв'язується за допомогою ітераційного методу. Нарешті, ми проводимо числове моделювання для перевірки теоретичного аналізу за допомогою Matlab.
dc.description.abstractIn this paper, we propose a mathematical model that describes the effect of rumors on the success of vaccination programs against Covid-19 in an environment infected by the coronavirus. The aim of this study is to highlight the role of addressing the spread of rumors regarding vaccination risks and booster doses in the success of vaccination programs and in achieving herd immunity. Additionally, we formulate an optimal control problem by proposing several strategies, including awareness and anti-rumor programs, to assist country officials in achieving successful vaccination programs with optimal effort. The existence of optimal controls is investigated, and Pontryagin's maximum principle is used to characterize them. The optimality system is solved using an iterative method. Finally, we conduct numerical simulations to verify the theoretical analysis using Matlab.
dc.format.extent250-263
dc.format.pages14
dc.identifier.citationThe impact of rumors on the success of Covid-19 vaccination programs in a Coronavirus-infected environment: optimal control approach / O. Balatif, A. Kouidere, D. Kada, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 250–263.
dc.identifier.citationenThe impact of rumors on the success of Covid-19 vaccination programs in a Coronavirus-infected environment: optimal control approach / O. Balatif, A. Kouidere, D. Kada, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 250–263.
dc.identifier.doi10.23939/mmc2024.01.250
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113785
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 11 (1), 2024
dc.relation.ispartofMathematical Modeling and Computing, 11 (1), 2024
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dc.relation.references[2] Zylberman P. L’histoire des anti-vaccin. Magazine Mutations. 24 (2018).
dc.relation.references[3] Kawachi K. Deterministic models for rumor transmission. Nonlinear Analysis: Real World Applications. 9 (5), 1989–2028 (2008).
dc.relation.references[4] Kosfeld M. Rumours and markets. Journal of Mathematical Economics. 41 (6), 646–664 (2005).
dc.relation.references[5] Status of COVID-19 Vaccines within WHO EUL/PQ evaluation process. https://www.who.int/emergencnies/diseases/novel-coronavirus-2019/covid-19-vaccines.
dc.relation.references[6] Study: On Twitter, false news travels faster than true stories. Research project finds humans, not bots, are primarily responsible for spread of misleading information. https://news.mit.edu/2018/study-twitter-false-news-travels-faster-true-stories-0308.
dc.relation.references[7] Daley D. J., Kendall D. G. Epidemics and Rumours. Nature. 204, 1118 (1964).
dc.relation.references[8] Daley D. J., Kendall D. G. Stochastic Rumours. IMA Journal of Applied Mathematics. 1 (1), 42–55 (1965).
dc.relation.references[9] Zhao X., Wang J. Dynamical Model about Rumor Spreading with Medium. Discrete Dynamics in Nature and Society. 2013, 586867 (2013).
dc.relation.references[10] El Bhih A., Ghazzali R., Ben Rhila S., Rachik M., El Alami Laaroussi A. A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network. Discrete Dynamics in Nature and Society. 2020, 4386476 (2020).
dc.relation.references[11] Musa S., Fori M. Mathematical Model of the Dynamics of Rumor Propagation. Journal of Applied Mathematics and Physics. 7 (6), 1289–1303 (2019).
dc.relation.references[12] Liu Y., Zeng C., Luo Y. Dynamics of a New Rumor Propagation Model with the Spread of Truth. Applied Mathematics. 9 (5), 536–549 (2018).
dc.relation.references[13] Wenkai C., Zhang H., Georgescu P., Li T., Bing Z. Taming obstinate spreaders: the dynamics of a rumor spreading model incorporating inhibiting mechanisms and attitude adjustment. Computational and Applied Mathematics. 40, 125 (2021).
dc.relation.references[14] Cheng Y., Huo L., Zhao L. Stability analysis and optimal control of rumor spreading model under media coverage considering time delay and pulse vaccination. Chaos, Solitons & Fractals. 157, 111931 (2022).
dc.relation.references[15] Huo L., Chen S., Xie X., Liu H., He J. Optimal Control of ISTR Rumor Propagation Model with Social Reinforcement in Heterogeneous Network. Complexity. 2021, 5682543 (2021).
dc.relation.references[16] Ghosh M., Das S., Das P. Dynamics and control of delayed rumor propagation through social networks. Journal of Applied Mathematics and Computing. 68, 3011–3040 (2021).
dc.relation.references[17] Kouidere A., Elhia M., Balatif O. A spatiotemporal spread of COVID-19 pandemic with vaccination optimal control strategy: A case study in Morocco. Mathematical Modeling and Computing. 10 (1), 171–185 (2023).
dc.relation.references[18] Yavorska O., Bun R. Spatial analysis of COVID-19 spread in Europe using “center of gravity” concept. Mathematical Modeling and Computing. 9 (1), 130–142 (2022).
dc.relation.references[19] Zuo C., Zhu F., Ling Y. Analyzing Covid-19 vaccination behavior using an SEIRM/V epidemic model with awareness decay. Frontiers in Public Health. 10, 817749 (2022).
dc.relation.references[20] Kiouach D., El-idrissi S. E. A., Sabbar Y. A mathematical study of the COVID-19 propagation through a stochastic epidemic model. Mathematical Modeling and Computing. 10 (3), 784–795 (2023).
dc.relation.references[21] Khajji B., Kouidere A., Elhia M., Balatif O., Rachik M. Fractional optimal control problem for an agestructured model of COVID-19 transmission. Chaos, Solitons & Fractals. 143, 110625 (2021).
dc.relation.references[22] Kouidere A., El Youssoufi L., Ferjouchia H., Balatif Omar., Rachik M. Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness. Chaos, Solitons & Fractals. 145, 110777 (2021).
dc.relation.references[23] Birkhoff G., Rota G. C. Ordinary Differential Equations. John Wiley & Sons, New York (1989).
dc.relation.references[24] Fleming W. H., Rishel R. W. Deterministic and Stochastic Optimal Control. Springer, New York (1975).
dc.relation.references[25] Boyce W. E., DiPrima R. C. Elementary Differential Equations and Boundary Value Problems. John Wiley & Sons, New York (2009).
dc.relation.references[26] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F. Mathematical Theory of Optimal Processes. Wiley, New York (1962).
dc.relation.referencesen[1] Riedel S. Edward Jenner and the history of smallpox and vaccination. Baylor University Medical Center Proceedings. 18 (1), 21–25 (2005).
dc.relation.referencesen[2] Zylberman P. L’histoire des anti-vaccin. Magazine Mutations. 24 (2018).
dc.relation.referencesen[3] Kawachi K. Deterministic models for rumor transmission. Nonlinear Analysis: Real World Applications. 9 (5), 1989–2028 (2008).
dc.relation.referencesen[4] Kosfeld M. Rumours and markets. Journal of Mathematical Economics. 41 (6), 646–664 (2005).
dc.relation.referencesen[5] Status of COVID-19 Vaccines within WHO EUL/PQ evaluation process. https://www.who.int/emergencnies/diseases/novel-coronavirus-2019/covid-19-vaccines.
dc.relation.referencesen[6] Study: On Twitter, false news travels faster than true stories. Research project finds humans, not bots, are primarily responsible for spread of misleading information. https://news.mit.edu/2018/study-twitter-false-news-travels-faster-true-stories-0308.
dc.relation.referencesen[7] Daley D. J., Kendall D. G. Epidemics and Rumours. Nature. 204, 1118 (1964).
dc.relation.referencesen[8] Daley D. J., Kendall D. G. Stochastic Rumours. IMA Journal of Applied Mathematics. 1 (1), 42–55 (1965).
dc.relation.referencesen[9] Zhao X., Wang J. Dynamical Model about Rumor Spreading with Medium. Discrete Dynamics in Nature and Society. 2013, 586867 (2013).
dc.relation.referencesen[10] El Bhih A., Ghazzali R., Ben Rhila S., Rachik M., El Alami Laaroussi A. A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network. Discrete Dynamics in Nature and Society. 2020, 4386476 (2020).
dc.relation.referencesen[11] Musa S., Fori M. Mathematical Model of the Dynamics of Rumor Propagation. Journal of Applied Mathematics and Physics. 7 (6), 1289–1303 (2019).
dc.relation.referencesen[12] Liu Y., Zeng C., Luo Y. Dynamics of a New Rumor Propagation Model with the Spread of Truth. Applied Mathematics. 9 (5), 536–549 (2018).
dc.relation.referencesen[13] Wenkai C., Zhang H., Georgescu P., Li T., Bing Z. Taming obstinate spreaders: the dynamics of a rumor spreading model incorporating inhibiting mechanisms and attitude adjustment. Computational and Applied Mathematics. 40, 125 (2021).
dc.relation.referencesen[14] Cheng Y., Huo L., Zhao L. Stability analysis and optimal control of rumor spreading model under media coverage considering time delay and pulse vaccination. Chaos, Solitons & Fractals. 157, 111931 (2022).
dc.relation.referencesen[15] Huo L., Chen S., Xie X., Liu H., He J. Optimal Control of ISTR Rumor Propagation Model with Social Reinforcement in Heterogeneous Network. Complexity. 2021, 5682543 (2021).
dc.relation.referencesen[16] Ghosh M., Das S., Das P. Dynamics and control of delayed rumor propagation through social networks. Journal of Applied Mathematics and Computing. 68, 3011–3040 (2021).
dc.relation.referencesen[17] Kouidere A., Elhia M., Balatif O. A spatiotemporal spread of COVID-19 pandemic with vaccination optimal control strategy: A case study in Morocco. Mathematical Modeling and Computing. 10 (1), 171–185 (2023).
dc.relation.referencesen[18] Yavorska O., Bun R. Spatial analysis of COVID-19 spread in Europe using "center of gravity" concept. Mathematical Modeling and Computing. 9 (1), 130–142 (2022).
dc.relation.referencesen[19] Zuo C., Zhu F., Ling Y. Analyzing Covid-19 vaccination behavior using an SEIRM/V epidemic model with awareness decay. Frontiers in Public Health. 10, 817749 (2022).
dc.relation.referencesen[20] Kiouach D., El-idrissi S. E. A., Sabbar Y. A mathematical study of the COVID-19 propagation through a stochastic epidemic model. Mathematical Modeling and Computing. 10 (3), 784–795 (2023).
dc.relation.referencesen[21] Khajji B., Kouidere A., Elhia M., Balatif O., Rachik M. Fractional optimal control problem for an agestructured model of COVID-19 transmission. Chaos, Solitons & Fractals. 143, 110625 (2021).
dc.relation.referencesen[22] Kouidere A., El Youssoufi L., Ferjouchia H., Balatif Omar., Rachik M. Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness. Chaos, Solitons & Fractals. 145, 110777 (2021).
dc.relation.referencesen[23] Birkhoff G., Rota G. C. Ordinary Differential Equations. John Wiley & Sons, New York (1989).
dc.relation.referencesen[24] Fleming W. H., Rishel R. W. Deterministic and Stochastic Optimal Control. Springer, New York (1975).
dc.relation.referencesen[25] Boyce W. E., DiPrima R. C. Elementary Differential Equations and Boundary Value Problems. John Wiley & Sons, New York (2009).
dc.relation.referencesen[26] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F. Mathematical Theory of Optimal Processes. Wiley, New York (1962).
dc.relation.urihttps://www.who.int/emergencnies/diseases/novel-coronavirus-2019/covid-19-vaccines
dc.relation.urihttps://news.mit.edu/2018/study-twitter-false-news-travels-faster-true-stories-0308
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectматематичне моделювання
dc.subjectоптимальний контроль
dc.subjectчутки
dc.subjectщеплення
dc.subjectCovid-19
dc.subjectmathematical modeling
dc.subjectoptimal control
dc.subjectrumors
dc.subjectvaccination
dc.subjectCovid-19
dc.titleThe impact of rumors on the success of Covid-19 vaccination programs in a Coronavirus-infected environment: optimal control approach
dc.title.alternativeВплив чуток на успіх програм вакцинації проти Covid-19 у зараженому коронавірусом середовищі: підхід оптимального керування
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 1