Analysis and comparative study of a deterministic mathematical model of SARS-COV-2 with fractal-fractional operators: a case study.

Comparison Data fitting Epidemic model Fractal-fractional model Parameters estimation SARS-CoV-2

Journal

Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288

Informations de publication

Date de publication:
18 Mar 2024
Historique:
received: 26 11 2023
accepted: 07 03 2024
medline: 19 3 2024
pubmed: 19 3 2024
entrez: 19 3 2024
Statut: epublish

Résumé

In this paper, we investigate a fractal-fractional-order mathematical model with the influence of hospitalized patients and the impact of vaccination with fractal-fractional operators. The respective derivatives are considered in the Caputo, Caputo Fabrizio, and Atangana-Baleanu senses of fractional order

Identifiants

pubmed: 38499671
doi: 10.1038/s41598-024-56557-6
pii: 10.1038/s41598-024-56557-6
doi:

Types de publication

Journal Article

Langues

eng

Sous-ensembles de citation

IM

Pagination

6431

Informations de copyright

© 2024. The Author(s).

Références

World Health Organization. https://www.who.int/emergencies/diseases/novel-coronavirus-2019/question-and-answers-hub/q-a-detail/coronavirus-disease-covid-19 . https://www.who.int/novel-corona-virus-2019 . Accessed 11 May 2020.
Bennett, G., Young, E., Butler, I. & Coe, S. The impact of lockdown during the COVID-19 outbreak on dietary habits in various population groups: A scoping review. Front. Nutr. 8, 626432 (2021).
doi: 10.3389/fnut.2021.626432 pubmed: 33748175 pmcid: 7969646
Di Domenico, L., Pullano, G., Sabbatini, C. E., Boëlle, P. Y. & Colizza, V. Impact of lockdown on COVID-19 epidemic in Île-de-France and possible exit strategies. BMC Med. 18(1), 1–13 (2020).
doi: 10.1186/s12916-020-01698-4
Le, T. T. et al. The COVID-19 vaccine development landscape. Nat. Rev. Drug Discov. 19(5), 305–306 (2020).
doi: 10.1038/d41573-020-00073-5
Grzybowski, J. M. V., Da Silva, R. V. & Rafikov, M. Expanded SEIRCQ model applied to COVID-19 epidemic control strategy design and medical infrastructure planning. Math. Probl. Eng. 20, 20 (2020).
Jahanshahi, H., Sajjadi, S. S., Bekiros, S. & Aly, A. A. On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller. Chaos Solitons Fractals 144, 110698 (2021).
doi: 10.1016/j.chaos.2021.110698
Center for Disease Control and Prevention (CDC). https://covid.cdc.gov/covid-data-tracker/#datatracker-home . https://www.cdc.gov/corona-virus . Accessed 3 Aug 2021.
Jin, F., Qian, Z. S., Chu, Y. M. & Ur Rahman, M. On nonlinear evolution model for drinking behavior under Caputo-Fabrizio derivative. J. Appl. Anal. Comput. 12(2), 790–806 (2022).
Kubra, K. T., Gulshan, S. & Ali, R. An Atangana–Baleanu derivative-based fractal-fractional order model for the monkey pox virus: A case study of USA. Partial Differ. Equ. Appl. Math. 20, 100623 (2024).
doi: 10.1016/j.padiff.2024.100623
Shah, K. et al. Fractal-fractional mathematical model addressing the situation of corona virus in Pakistan. Results Phys. 19, 103560 (2020).
doi: 10.1016/j.rinp.2020.103560 pubmed: 33200064 pmcid: 7658553
Li, B., Zhang, T. & Zhang, C. Investigation of financial bubble mathematical model under fractal-fractional Caputo derivative. FRACTALS (fractals) 31(05), 1–13 (2023).
Li, P. et al. Dynamical properties of a meminductor chaotic system with fractal-fractional power law operator. Chaos Solitons Fractals 175, 114040 (2023).
doi: 10.1016/j.chaos.2023.114040
Fatima, B., Yavuz, M., Ur Rahman, M. & Al-Duais, F. S. Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control. Math. Biosci. Eng. 20(7), 11847–11874 (2023).
doi: 10.3934/mbe.2023527 pubmed: 37501423
Fatima, B., Yavuz, M., Ur Rahman, M., Althobaiti, A. & Althobaiti, S. Predictive modeling and control strategies for the transmission of middle east respiratory syndrome coronavirus. Math. Comput. Appl. 28(5), 98 (2023).
Kubra, K. T. & Ali, R. Modeling and analysis of novel COVID-19 outbreak under fractal-fractional derivative in Caputo sense with power-law: A case study of Pakistan. Model. Earth Syst. Environ. 20, 1–18 (2023).
Atangana, A. & Qureshi, S. Modeling attractors of chaotic dynamical systems with fractal-fractional operators. Chaos Solitons Fractals 123, 320–337 (2019).
doi: 10.1016/j.chaos.2019.04.020
Ahmed, I., Modu, G. U., Yusuf, A., Kumam, P. & Yusuf, I. A mathematical model of corona-virus Disease (COVID-19) containing asymptomatic and symptomatic classes. Results Phys. 21, 103776 (2021).
doi: 10.1016/j.rinp.2020.103776 pubmed: 33432294 pmcid: 7787076
Tartof, S. Y. et al. Effectiveness of a third dose of BNT162b2 mRNA COVID-19 vaccine in a large US health system: A retrospective cohort study. Lancet Region. Health-Am. 9, 100198 (2022).
doi: 10.1016/j.lana.2022.100198
Hethcote, H. W. The mathematics of infectious diseases. SIAM Rev. 42(4), 599–653 (2000).
doi: 10.1137/S0036144500371907
Pakistan recorded corona-virus Cases since the epidemic began, according to the COVID-19 health advisory platform by ministry of national health services regulations and coordinations. Government of Pakistan. Accessed 21 May 2020.
Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. On the definition and the computation of the basic reproduction ratio [Formula: see text] in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28(4), 365–382 (1990).
doi: 10.1007/BF00178324 pubmed: 2117040
Obasi, C. & Mbah, G. C. E. On the stability analysis of a mathematical model of lassa fever disease dynamics. J. Nigerian Soc. Math. Biol. 2, 135–144 (2019).
Van den Driessche, P. & Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1–2), 29–48 (2002).
doi: 10.1016/S0025-5564(02)00108-6 pubmed: 12387915
Caputo, M. Linear models of dissipation whose Q is almost frequency independent-II. Geophys. J. Int. 13(5), 529–539 (1967).
doi: 10.1111/j.1365-246X.1967.tb02303.x
Caputo, M. & Fabrizio, M. A new definition of fractional derivative without singular kernel. Progress Fract. Differ. Appl. 1(2), 73–85 (2015).
Atangana, A., & Baleanu, D. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. arXiv:1602.03408 (arXiv preprint) (2016).
Arif, M., Kumam, P., Kumam, W., Akgul, A. & Sutthibutpong, T. Analysis of newly developed fractal-fractional derivative with power law kernel for MHD couple stress fluid in channel embedded in a porous medium. Sci. Rep. 11(1), 20858 (2021).
doi: 10.1038/s41598-021-00163-3 pubmed: 34675245 pmcid: 8531019
Ali, Z., Rabiei, F., Shah, K. & Khodadadi, T. Qualitative analysis of fractal-fractional order COVID-19 mathematical model with case study of Wuhan. Alex. Eng. J. 60(1), 477–489 (2021).
doi: 10.1016/j.aej.2020.09.020
Arfan, M., Shah, K. & Ullah, A. Fractal-fractional mathematical model of four species comprising of prey-predation. Phys. Scr. 96(12), 124053 (2021).
doi: 10.1088/1402-4896/ac2f37
Ghanbari, B. & Gómez-Aguilar, J. F. Analysis of two avian influenza epidemic models involving fractal-fractional derivatives with power and Mittag–Leffler memories. Chaos Interdiscip. J. Nonlinear Sci. 29(12), 123113 (2019).
doi: 10.1063/1.5117285
Jeelani, M. B. et al. Mathematical modeling and forecasting of COVID-19 in Saudi Arabia under fractal-fractional derivative in caputo sense with power-law. Axioms 10(3), 228 (2021).
doi: 10.3390/axioms10030228
Qu, H. et al. Investigating fractal-fractional mathematical model of tuberculosis (TB) under fractal-fractional caputo operator. Fractals 30(05), 2240126 (2022).
doi: 10.1142/S0218348X22401260
Sweilam, N. H., Al-Mekhlafi, S. M. & Almutairi, A. Fractal fractional optimal control for a novel malaria mathematical model; a numerical approach. Results Phys. 19, 103446 (2020).
doi: 10.1016/j.rinp.2020.103446

Auteurs

Khadija Tul Kubra (KT)

Department of Mathematics, Government College University, Faisalabad, Punjab, 38040, Pakistan.

Rooh Ali (R)

Department of Mathematics, Government College University, Faisalabad, Punjab, 38040, Pakistan. roohali@gcuf.edu.pk.

Rubayyi Turki Alqahtani (RT)

Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University(IMSIU), Riyadh, Saudi Arabia. rtalqahtani@imamu.edu.sa.

Samra Gulshan (S)

Department of Mathematics, Government College University, Faisalabad, Punjab, 38040, Pakistan.

Zahoor Iqbal (Z)

College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, China.

Classifications MeSH