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Research Article

Mathematical modeling of corona virus (COVID-19) and stability analysis

ORCID Icon, , , ORCID Icon &
Pages 1114-1133 | Received 23 Feb 2022, Accepted 24 Jul 2022, Published online: 10 Aug 2022

References

  • Allegretti S, Bulai IM, Marino R, Menandro MA, Parisi K. 2021. Vaccination effect conjoint to fraction of avoided contacts for a Sars-Cov-2 mathematical model. MMNSA. 1(2):56–66.
  • Atangana A, Baleanu, D. 2016. New fractional derivatives with non-local and non-singular kernels. Therm Sci. 20(2):763–769.
  • Atangana A, Khan MA, Fatmawati. 2020. Modeling and analysis of competition model of bank data with fractal-fractional Caputo-Fabrizio operator. Alexandria Engin J. 59(4):1985–1998.
  • Atangana A. 2017. Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system. Chaos, Solitons Fractals. 102:396–406.
  • Bonyah E, Yavuz M, Baleanu D, Kumar S. 2022. A robust study on the listeriosis disease by adopting fractal-fractional operators. Alexandria Engin J. 61(3):2016–2028.
  • Coronavirus (COVID-19) Mortality Rate (MR). 2020. 5 March 2020. Retrieved 23 March 2020. www.worldometers.info.
  • Coronavirus Disease. 2019. (COVID-19) https://www.cdc.gov/dotw/covid-19/. 17 March 2020. Retrieved 23 March 2020.
  • Dabasi B. 2021. Stability analysis of an incommensurate fractional-order SIR model. Math Model Numer Simulation with Appl. 1(1):44–55.
  • Ganesh A, Deepa S, Baleanu D, Santra SS, Moaaz O, Govindan V, Ali R. 2022. Hyers-Ulam-Mittag-Leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform. MATH. 7(2):1791–1810.
  • Hattaf K, Yousfi N. 2020. Dynamics of SARS-CoV-2 infection model with two models of transmission and immune response. Math Biosci Eng. 17(5):5326–5340.
  • Hattaf K. 2020. A new generalized definition of fractional derivative with non-singular kernel. Computation. 8(2):49.
  • Hattaf K. 2021. Stability of fractional differential equations with new generalized Hattaf fractional derivative. Math Prob Eng. 2021:8608447.
  • Hui DS, I Azhar E, Madani TA, Ntoumi F, Kock R, Dar O, Ippolito G, Mchugh TD, Memish ZA, Drosten C, et al. 2020. The continuing 2019-nCoV epidemic threat of novel coronaviruses to global health-The latest 2019 novel coronavirus outbreak in Wuhan, China. Int J Infect Dis. 91:264–266.
  • Ikram R, Khan A, Zahri M, Saeed A, Yavuz M, Kumam P. 2022. Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay. Comput Biol Med. 141:105115.
  • Khan KA, Butt AR, Raza N, Maqbool K. 2019. Unsteady magneto- hydrodynamics flow between two orthogonal moving plates. Eur Phys J Plus. 134:1. doi:10.1140/epjp/i2019-12286-x
  • Khan KA, Butt AR, Raza N. 2018. Effects of heat and mass transfer on unsteady boundary layer flow of a chemical reacting casson fluid. Results Phys. 8:610–620.
  • Khan KA, Jamil F, Ali J, Khan I, Ahmad N, Andualem M, Rafiq M. 2022. Analytical simulation of heat and mass transmission in casson fluid flow across a stretching surface. Math Prob Eng. 2022:5576194.
  • Khan KA, Raza N, Inc M. 2021. Insights of numerical simulations of magnetohydrodynamic squeezing nanofluid flow through a channel with permeable walls. Propul Power Res. 10(4):412–420.
  • Khan KA, Seadawy AR, Raza N. 2022. The homotopy simulation of MHD time dependent three dimensional shear thining fluid flow over a stretching plate. Chaos, Solitons and Fractals. 157:111888.
  • Khan MA, Atangana A. 2020. Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alexandria Engin J. 59(4):2379–2389.
  • Khan MA, Ullah S, Farhan M. 2019. The dynamics of Zika virus with Caputo fractional derivative. AIMS Mathematics. 4(1):134–146.
  • Li Q, Guan X, Wu P, Wang X, Zhou L, Tong Y, Ren R, Leung KSM, Lau EHY, Wong JY, et al. 2020. Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia. N Engl J Med. 382(13):1199–1207.
  • Li XP, Gul N, Khan MA, Bilal R, Ali A, Alshahrani MY, Muhammad T, Islam, S, 29. 2021. A new Hepatitis B model in light of asymptomatic carriers and vaccination study through Atangana-Baleanu derivative. Results Phys. 29:104603.
  • Li X-P, Wang Y, Khan MA, Alshahrani MY, Muhammad T. 2021. A dynamical study of SARS-COV-2: A study of third wave. Results Phys. 29:104705.
  • Li YX, Muhammad T, Bilal M, Khan MA, Ahmadian A, Pansera BA. 2021. Fractional simulation for Darcy-Forchheimer hybrid nanoliquid flow with partial slip over a spinning disk. Alexandria Engin J. 60(5):4787–4796.
  • Li Z, Liu Z, Khan MA. 2019. Fractional investigation of bank data with fractal fractional Caputo derivative. Chaos, Solitons and Fractals. 131:109528. doi:10.1016/j.chaos.2019.109528
  • Ming WK, Huang J, Zhang CJ. 2020. Breaking down of healthcare system: Mathematical modelling for controlling the novel coronavirus (2019-nCoV) outbreak in Wuhan. China. doi: 10.1101/2020.01.27.922443
  • Naik PA, Yavuz M, Qureshi S, Zu J, Townley S. 2020. Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. Eur Phys J Plus. 135(10):1–42.
  • Naming the coronavirus disease (COVID-19) and the virus that causes it, World Health Organization (WHO). 2020. https://www.who.int/emergencies/diseases/novel-coronavirus-2019/technical-guidance/naming-the-coronavirus-disease-(covid-2019)-and-the-virus-that-causes-it. Archived from the original on 28 February 2020. Retrieved 28 February 2020.
  • Nesteruk I. 2020. Statistics based predictions of coronavirus 2019-nCoV spreading in mainland China. Innov Biosyst Bioeng. 4(1):13–18.
  • Oskose F, Yavuz M. 2021. Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey. Comput Biol Med. 141:105044. doi:10.1016/j.compbiomed.2021.105044
  • Özköse F, Yavuz M, Şenel MT, Habbireeh R. 2022. Fractional order modelling of Omicorn, SARS-CoV-2 variant containing heart attack effects using real data from the United Kingdom. Chaos, Solitons and Fractals. 157:111954. doi:10.1016/j.chaos.2022.111954.
  • QA on coronaviruses, World Health Organization. 2020. 11 February 2020. Retrieved 24 February 2020.
  • Raza N, Arshed S, Ali Khan K, Inc M. 2021. Fractional soliton dynamics of electrical microtubule transmission line model with local M-derivative. Commun Theor Phys. 73(9):095002.
  • Raza N, Arshed S, Khan KA, Baleanu D. 2021. New and more fractional soliton solutions related to generalised Davey-Stewartson equation using oblique wave transformation. Mod Phys Lett B. 35(19):2150317.
  • Shen SH, Chu YM, Khan MA, Muhammad S, Hartomy OA, Higazy M. 2021. Mathematical modeling and optimal control of the COVID-19 dynamics. Results Phys. 31:105028.
  • van den Driessche P, Watmough J. 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosci. 180(1–2):29–48.
  • Wang W, Khan MA. 2020. Analysis and numerical simulation of fractional model of bank data with fractal–fractional Atangana–Baleanu derivative. J Comput Appl Mathematics. 369:112646.
  • WHO Director-General's opening remarks at the media briefing on COVID-19. 2020. World Health Organization (WHO) (Press release). https://www.who.int/director-general/speeches/detail/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19. 11 March 2020. Retrieved 12 March 2020.
  • Wu JT, Leung K, Leung GM. 2020. New casting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. Lancent. 6736(20):30260–30269.
  • Yavuz M, Coşar FÖ, Günay F, Özdemir FN. 2021. A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign. OJMSi. 09(03):299–321.
  • Zafar ZA, Mushtaq M, Rehan K. 2018. A non-integer order dengue internal transmission model. Adv Difference Equations. 2018:23.
  • Zafar ZA, Rehan K, Mushtaq M. 2017. HIV/AIDS epidemic fractional-order model. J Difference Equations Appl. 23(7):1298–1315.
  • Zafar ZA, Younas S, Zaib S, Tunc C. 2022. An efficient numerical simulation and mathematical modelling for prevention of tuberculosis. Int J Biomath. 15(04):2250015. Art
  • Zhao S, Lin Q, Ran J, Musa SS, Yang G, Wang W, Lou Y, Gao D, Yang L, He D, et al. 2020. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: a data-driven analysis in the early phase of the outbreak. Int J Infect Dis. 92:214–217.
  • Zhao S, Musa SS, Lin Q, Ran J, Yang G, Wang W, Lou Y, Yang L, Gao D, He D, et al. 2020. Estimating the unreported number of novel coronavirus (2019-nCoV) cases in China in the first half of January 2020: a data-driven Modelling analysis of the early outbreak. JCM. 9(2):388.

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