Fractional-order mathematical model for analysing impact of quarantine on transmission of COVID-19 in India

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dc.citation.epage266
dc.citation.issue2
dc.citation.spage253
dc.contributor.affiliationУніверситет Свамі Рамананда Тірта Маратвади
dc.contributor.affiliationІнженерний коледж А. С. Патил
dc.contributor.affiliationШиваджі Махавідялая
dc.contributor.affiliationSwami Ramanand Teerth Marathwada University
dc.contributor.affiliationA. C. Patil College of Engineering
dc.contributor.affiliationShivaji Mahavidyalaya
dc.contributor.authorПавар, Д. Д.
dc.contributor.authorПатил, В. Д.
dc.contributor.authorРаут, Д. К.
dc.contributor.authorPawar, D. D.
dc.contributor.authorPatil, W. D.
dc.contributor.authorRaut, D. K.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-10-24T07:21:45Z
dc.date.available2023-10-24T07:21:45Z
dc.date.created2021-03-01
dc.date.issued2021-03-01
dc.description.abstractВперше про спалах нової коронавірусної інфекції повідомили у місті Ухань, Китай, у грудні 2019 року. В Індії про перший випадок було повідомлено 30 січня 2020 року, це була особа з історією переміщень до інфікованої країни. Беручи до уваги факт густонаселеної та диверсифікованої країни, такої як Індія, запропоновано нову математичну модель дробового порядку, щоб визначити динамiку поширення коронавiрусної хвороби (COVID-19) та стратегію її контролю в Індії. Класична модель SEIR застосована до трьох секцій населення, а саме: мігранти на карантині, безсимптомні мігранти не переміщені на карантин та місцеве населення, яке уряд Індії піддав блокуванню в зоні стримування для запобігання розповсюдженню хвороби в Індії. Також враховано фізичну взаємодію між ними для оцінки динаміки поширення коронавірусу. Встановлено базове репродуктивне число (R0) для визначення заражуваності COVID-19. Чисельне моделювання проведено за допомогою узагальненого методу Ейлера. Щоб перевiрити актуальність нашого аналізу, ми дослідили деякі чисельні моделювання для різного дробового порядку, змінюючи значення параметрів за допомогою MATLAB, щоб дослідження відповідало реалістичному сценарію пандемії.
dc.description.abstractAn outbreak of the novel coronavirus disease was first reported in Wuhan, China in December 2019. In India, the first case was reported on January 30, 2020 on a person with a travel history to an affected country. Considering the fact of a heavily populated and diversified country like India, we have proposed a novel fractional-order mathematical model to elicit the transmission dynamics of the coronavirus disease (COVID-19) and the control strategy for India. The classical SEIR model is employed in three compartments, namely: quarantined immigrated population, non-quarantined asymptomatic immigrated population, and local population subjected to lockdown in the containment areas by the government of India to prevent the spread of disease in India. We have also taken into account the physical interactions between them to evaluate the coronavirus transmission dynamics. The basic reproduction number (R0) has been derived to determine the communicability of the disease. Numerical simulation is done by using the generalised Euler method. To check the feasibility of our analysis, we have investigated some numerical simulations for various fractional orders by varying values of the parameters with help of MATLAB to fit the realistic pandemic scenario.
dc.format.extent253-266
dc.format.pages14
dc.identifier.citationPawar D. D. Fractional-order mathematical model for analysing impact of quarantine on transmission of COVID-19 in India / D. D. Pawar, W. D. Patil, D. K. Raut // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 2. — P. 253–266.
dc.identifier.citationenPawar D. D. Fractional-order mathematical model for analysing impact of quarantine on transmission of COVID-19 in India / D. D. Pawar, W. D. Patil, D. K. Raut // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 2. — P. 253–266.
dc.identifier.doidoi.org/10.23939/mmc2021.02.253
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60381
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 2 (8), 2021
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dc.relation.references[11] Samko S. G., Kilbas A. A., Marichev Q. I. Fractional Integrals and Derivatives Theory and Applications. Gorden and Breach, New York (1993).
dc.relation.references[12] Podlubny I. Fractional Differential Equation. Academic Press, New York (1999).
dc.relation.references[13] Pawar D. D., Patil W. D., Raut D. K. Numerical solution of fractional order mathematical model of drug resistant tuberculosis with two line treatment. Journal Mathematics and Computational Science. 10 (2), 262–276 (2019).
dc.relation.references[14] Kumar D., Singh J., Qurashi M. A., Baleanu D. A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying. Advances in Difference Equations. 2019, Article number: 278 (2019).
dc.relation.references[15] Pawar D. D., Patil W. D., Raut D. K. Analysis of malaria dynamics using its fractional order mathematical model. Journal of Applied Mathematics and Informatics. 39 (1-2), 197–214 (2021).
dc.relation.references[16] Shaikh A. S., Shaikh I. N., Nisar K. S. A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control. Advances in Difference Equations. 2020, 373 (2020).
dc.relation.references[17] Khan M. A., Ullah S., Farooq M. A new fractional model for tuberculosis with relapse via Atangana–Baleanu derivative. Chaos, Solitons & Fractals. 116, 227–238 (2018).
dc.relation.references[18] Khan M. A., Atangana A. Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alexandria Engineering Journal. 59 (4), 2379–2389 (2020).
dc.relation.references[19] Mohamed A. S., Mahmoud R. A. Picard, Adomian and predictor corrector methods for an initial value problem of arbitrary (fractional) orders differential equation. Journal of the Egyptian Mathematical Society. 24 (2), 165–170 (2016).
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dc.relation.references[21] Biswas S. K., Ghosh J. K., Sarkar S. COVID-19 pandemic in India: a mathematical model study. Nonlinear dynamics. 102 (1), 537–553 (2020).
dc.relation.references[22] Chatterjee K., Chatterjee K., Yadav A. K., Subramanian S. Healthcare impact of COVID-19 epidemic in India: A stochastic mathematical model. Medical Journal Armed Forces India. 76 (2), 147–155 (2020).
dc.relation.referencesen[1] World Health Organization. Pneumonia of unknown cause - China, Emergenciespreparedness, response, Disease outbreak news. World Health Organization(WHO). https://www.who.int/csr/don/05-january-2020-pneumonia-of-unkown-cause-china/en/ (2020).
dc.relation.referencesen[2] World Health Organization. Laboratory testing for 2019 novel coronavirus (2019-nCoV) in suspected human cases. World Health Organization(WHO). https://www.who.int/health-topics/coronavirus/laboratory-diagnostics-for-novel-coronavirus (2020).
dc.relation.referencesen[3] Lin Q., Zhao S., Gao D., Lou Y., Yang S., Musa S. S., Wang M. H., Cai Y., Wang W., Yang L., He D. A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action. International journal of infectious diseases. 93, 211–216 (2020).
dc.relation.referencesen[4] Wuhan Municipal Health Commission, China. New press and situation reports of the pneumonia caused by novel coronavirus from December 31, 2019 to January 21, 2020 released by the Wuhan municipal health commission, China (2020). http://wjw.wuhan.gov.cn/front/web/list2nd/no/710
dc.relation.referencesen[5] Rothana H. A., Byrareddy S. N. The epidemiology and pathogenesis of coronavirus disease (COVID-19) outbreak. Journal of Autoimmunity. 109, 102433 (2020).
dc.relation.referencesen[6] https://www.mygov.in/covid-19, June 06, 2020.
dc.relation.referencesen[7] Victor A. Mathematical predictions for COVID-19 as a global pandemic. Available at SSRN: https://ssrn.com/abstract=3555879 (2020).
dc.relation.referencesen[8] Ivorra B., Ferr´andez M. R., Vela-P´erez M., Ramos A. M. Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China. Communication Nonlinear Science and Numerical Simulations. 88, 205303 (2020).
dc.relation.referencesen[9] Tuite A. R., Fisman D. N., Greer A. L. Mathematical modelling of COVID-19 transmission and mitigation strategies in the population of Ontario, Canada. medRxiv (2020).
dc.relation.referencesen[10] Chen T.-M., Rui J., Wang Q. P., Zhao Z.-Y., Cui J.-A., Yin L. A mathematical model for simulating the phase-based transmissibility of a novel coronavirus. Infectious Diseases of Poverty. 9, Article number: 24 (2020).
dc.relation.referencesen[11] Samko S. G., Kilbas A. A., Marichev Q. I. Fractional Integrals and Derivatives Theory and Applications. Gorden and Breach, New York (1993).
dc.relation.referencesen[12] Podlubny I. Fractional Differential Equation. Academic Press, New York (1999).
dc.relation.referencesen[13] Pawar D. D., Patil W. D., Raut D. K. Numerical solution of fractional order mathematical model of drug resistant tuberculosis with two line treatment. Journal Mathematics and Computational Science. 10 (2), 262–276 (2019).
dc.relation.referencesen[14] Kumar D., Singh J., Qurashi M. A., Baleanu D. A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying. Advances in Difference Equations. 2019, Article number: 278 (2019).
dc.relation.referencesen[15] Pawar D. D., Patil W. D., Raut D. K. Analysis of malaria dynamics using its fractional order mathematical model. Journal of Applied Mathematics and Informatics. 39 (1-2), 197–214 (2021).
dc.relation.referencesen[16] Shaikh A. S., Shaikh I. N., Nisar K. S. A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control. Advances in Difference Equations. 2020, 373 (2020).
dc.relation.referencesen[17] Khan M. A., Ullah S., Farooq M. A new fractional model for tuberculosis with relapse via Atangana–Baleanu derivative. Chaos, Solitons & Fractals. 116, 227–238 (2018).
dc.relation.referencesen[18] Khan M. A., Atangana A. Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alexandria Engineering Journal. 59 (4), 2379–2389 (2020).
dc.relation.referencesen[19] Mohamed A. S., Mahmoud R. A. Picard, Adomian and predictor corrector methods for an initial value problem of arbitrary (fractional) orders differential equation. Journal of the Egyptian Mathematical Society. 24 (2), 165–170 (2016).
dc.relation.referencesen[20] Sarkar K., Khajanchi S., Nieto J. J. Modeling and forecasting the COVID-19 pandemic in India. Chaos, Solitons and Fractals. 139, 110049 (2020).
dc.relation.referencesen[21] Biswas S. K., Ghosh J. K., Sarkar S. COVID-19 pandemic in India: a mathematical model study. Nonlinear dynamics. 102 (1), 537–553 (2020).
dc.relation.referencesen[22] Chatterjee K., Chatterjee K., Yadav A. K., Subramanian S. Healthcare impact of COVID-19 epidemic in India: A stochastic mathematical model. Medical Journal Armed Forces India. 76 (2), 147–155 (2020).
dc.relation.urihttps://www.who.int/csr/don/05-january-2020-pneumonia-of-unkown-cause-china/en/
dc.relation.urihttps://www.who.int/health-topics/coronavirus/laboratory-diagnostics-for-novel-coronavirus
dc.relation.urihttp://wjw.wuhan.gov.cn/front/web/list2nd/no/710
dc.relation.urihttps://www.mygov.in/covid-19
dc.relation.urihttps://ssrn.com/abstract=3555879
dc.rights.holder© Національний університет “Львівська політехніка”, 2021
dc.subjectCOVID-19
dc.subjectепідемія
dc.subjectматематична модель дробового порядку (ММДБ)
dc.subjectчисло відтворення
dc.subjectузагальнений метод Ейлера (УМЕ)
dc.subjectCOVID-19
dc.subjectepidemic
dc.subjectfractional-order mathematical model (FOMM)
dc.subjectreproduction number
dc.subjectgeneralised Euler method (GEM)
dc.titleFractional-order mathematical model for analysing impact of quarantine on transmission of COVID-19 in India
dc.title.alternativeМатематична модель дробового порядку для аналізу впливу карантину на поширення COVID-19 в Індії
dc.typeArticle

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Mathematical Modeling And Computing. – 2021. – Vol. 8, No. 2