Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

Yıl 2022, , 228 - 243, 30.12.2022

Saeed Ahmad Dong Qiu Mati Ur Rahman

https://doi.org/10.53391/mmnsa.2022.019

Cited By: 7

Öz

For the sake of human health, it is crucial to investigate infectious diseases including HIV/AIDS, hepatitis, and others. Worldwide, the recently discovered new coronavirus (COVID-19) poses a serious threat. The experimental vaccination and different COVID-19 strains found around the world make the virus' spread unavoidable. In the current research, fractional order is used to study the dynamics of a nonlinear modified COVID-19 SEIR model in the framework of the Caputo-Fabrizio fractional operator with order b. Fixed point theory has been used to investigate the qualitative analysis of the solution respectively. The well-known Laplace transform method is used to determine the approximate solution of the proposed model. Using the COVID-19 data that is currently available, numerical simulations are run to validate the necessary scheme and examine the dynamic behavior of the various compartments of the model. In order to stop the pandemic from spreading, our findings highlight the significance of taking preventative steps and changing one's lifestyle.

Anahtar Kelimeler

COVID-19 model, theoretical analysis, Laplace transform, Caputo-Fabrizio fractional operator, numerical simulations

Kaynakça

• World Health Organization, Coronavirus disease 2019 (COVID-19) Situation Report-62 https : //www.who.int/docs/default –source/coronaviruse/situation – reports/20200322 – sitrep – 62 – covid – 19.pdf?sfvrsn = f7764c462, 2020.
• Lu, H., Stratton, C.W., & Tang, Y.W. Outbreak of pneumonia of unknown etiology in Wuhan, China: The mystery and the miracle. Journal of Medical Virology, 92(4), 401-402, (2020).
• Uçar, S. Analysis of hepatitis B disease with fractal–fractional Caputo derivative using real data from Turkey. Journal of Computational and Applied Mathematics, 419, 114692, (2023).
• Uçar, E., Özdemir, N., & Altun, E. Qualitative analysis and numerical simulations of new model describing cancer. Journal of Computational and Applied Mathematics, 422, 114899, (2023).
• Evirgen, F. Transmission of Nipah virus dynamics under Caputo fractional derivative. Journal of Computational and Applied Mathematics, 418, 114654, (2023).
• Özköse, F., Yavuz, M., Şenel, M.T., & Habbireeh, R. Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom. Chaos, Solitons & Fractals, 157, 111954, (2022).
• Joshi, H., Jha, B.K., & Yavuz, M. Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data. Mathematical Biosciences and Engineering, 20(1), 213-240, (2023).
• Allegretti, S., Bulai, I.M., Marino, R., Menandro, M.A., & Parisi, K. Vaccination effect conjoint to fraction of avoided contacts for a Sars-Cov-2 mathematical model. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 56-66, (2021).
• Haq, I.U., Ali, N., & Nisar, K.S. An optimal control strategy and Grünwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model. Mathematical Modelling and Numerical Simulation with Applications, 2(2), 108-116, (2022).
• He, F., Deng, Y., & Li, W. Coronavirus disease 2019: What we know?. Journal of medical virology, 92(7), 719-725, (2020).
• Tian, X., Li, C., Huang, A., Xia, S., Lu, S., Shi, Z., ... & Ying, T. Potent binding of 2019 novel coronavirus spike protein by a SARS coronavirus-specific human monoclonal antibody. Emerging microbes & infections, 9(1), 382-385, (2020).
• Riou, J., & Althaus, C.L. Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020. Eurosurveillance, 25(4), 2000058, (2020).
• Li, B., Liang, H., & He, Q. Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model. Chaos, Solitons & Fractals, 146, 110856, (2021).
• Eskandari, Z., Avazzadeh, Z., Khoshsiar Ghaziani, R., & Li, B. Dynamics and bifurcations of a discrete-time Lotka–Volterra model using nonstandard finite difference discretization method. Mathematical Methods in the Applied Sciences, (2022).
• Li, B., Liang, H., Shi, L., & He, Q. Complex dynamics of Kopel model with nonsymmetric response between oligopolists. Chaos, Solitons & Fractals, 156, 111860, (2022).
• Qu, H., Rahman, M.U., Wang, Y., Arfan, M., & Adnan. Modeling Fractional-Order Dynamics of Mers-Cov via Mittag-Leffler Law. Fractals, 30(1), 2240046, (2022).
• Mekonen, K.G., Habtemicheal, T.G., & Balcha, S.F. Modeling the effect of contaminated objects for the transmission dynamics of COVID-19 pandemic with self protection behavior changes. Results in Applied Mathematics, 9, 100134, (2021).
• Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. Theory and applications of fractional differential equations (Vol.204). Elsevier, (2006).
• Samko, S.G., Kilbas, A.A., & Marichev, O.I. Fractional integrals and derivatives: theory and applications (Vol.1). Switzerland: Gordon and Breach Science Publishers, Yverdon, (1993).
• Haq, I.U., Yavuz, M., Ali, N., & Akgül, A. A SARS-CoV-2 fractional-order mathematical model via the modified Euler method. Mathematical and Computational Applications, 27(5), 82, (2022).
• Ucar, S., Evirgen, F., Özdemir, N., & Hammouch, Z. Mathematical analysis and simulation of a giving up smoking model within the scope of non-singular derivative. Proceeding of the Institute of Mathematics and Mechanics, 48, 84-99, (2022).
• Uçar, E., Uçar, S., Evirgen, F., & Özdemir, N. A fractional SAIDR model in the frame of Atangana–Baleanu derivative. Fractal and Fractional, 5(2), 32, (2021).
• Hilfer, R. (Ed.). Applications of fractional calculus in physics. World scientific, (2000).
• Uçar, S. Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives. Amer Inst Mathematical Sciences-AIMS, 14(7), 2571-2589, (2021).
• Sene, N. Theory and applications of new fractional-order chaotic system under Caputo operator. An International Journal of Optimization and Control, 12(1), 20-38, (2022).
• Zhang, L., ur Rahman, M., Haidong, Q., & Arfan, M. Fractal-fractional Anthroponotic Cutaneous Leishmania model study in sense of Caputo derivative. Alexandria Engineering Journal, 61(6), 4423-4433, (2022).
• Caputo, M., & Fabrizio, M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73-85, (2015).
• Atangana, A., & Alkahtani, B.S.T. Analysis of the Keller–Segel model with a fractional derivative without singular kernel. Entropy, 17(6), 4439-4453, (2015).
• Koca, I. Analysis of rubella disease model with non-local and non-singular fractional derivatives. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 8(1), 17-25, (2018).
• Baleanu, D., Mohammadi, H., & Rezapour, S. A mathematical theoretical study of a particular system of Caputo–Fabrizio fractional differential equations for the Rubella disease model. Advances in Difference Equations, 2020(1), 1-19, (2020).
• Abro, K.A., & Atangana, A. A comparative analysis of electromechanical model of piezoelectric actuator through Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. Mathematical Methods in the Applied Sciences, 43(17), 9681-9691, (2020).
• Morales-Delgado, V.F., Gómez-Aguilar, J.F., Saad, K., & Escobar Jiménez, R.F. Application of the Caputo-Fabrizio and Atangana-Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect. Mathematical Methods in the Applied Sciences, 42(4), 1167-1193, (2019).
• Chasreechai, S., Sitthiwirattham, T., El-Shorbagy, M.A., Sohail, M., Ullah, U., & ur Rahman, M. Qualitative theory and approximate solution to a dynamical system under modified type Caputo-Fabrizio derivative. AIMS Mathematics, 7(8), 14376-14393, (2022).
• Nisar, K.S., Ahmad, S., Ullah, A., Shah, K., Alrabaiah, H., & Arfan, M. Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data. Results in Physics, 21, 103772, (2021).
• Ameen, I.G., Sweilam, N.H., & Ali, H.M. A fractional-order model of human liver: Analytic-approximate and numerical solutions comparing with clinical data. Alexandria Engineering Journal, 60(5), 4797-4808, (2021).
• Xu, C., Ur Rahman, M., Fatima, B., & Karaca, Y. Theoretical and numerical investigation of complexities in fractional-order chaotic system having torus attractors, Fractals, 30(07), 2250164, (2022).
• Shah, K., Ali, A., Zeb, S., Khan, A., Alqudah, M.A., & Abdeljawad, T. Study of fractional order dynamics of nonlinear mathematical model. Alexandria Engineering Journal, 61(12), 11211-11224, (2022).
• Shah, K., Jarad, F., & Abdeljawad, T. On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative. Alexandria Engineering Journal, 59(4), 2305-2313, (2020).
• Liu, X., ur Rahman, M., Ahmad, S., Baleanu, D., & Nadeem Anjam, Y. A new fractional infectious disease model under the non-singular Mittag–Leffler derivative. Waves in Random and Complex Media, 1-27, (2022).
• Rahman, M.U., Arfan, M., Deebani, W., Kumam, P., & Shah, Z. Analysis of time-fractional Kawahara equation under Mittag-Leffler Power Law. Fractals, 30(1), 2240021, (2022).
• Rahman, M.U., Althobaiti, A., Riaz, M.B., & Al-Duais, F.S. A theoretical and numerical study on fractional order biological models with Caputo-Fabrizio derivative. Fractal and Fractional, 6(8), 446, (2022).
• Rashid, S., Hammouch, Z., Aydi, H., Ahmad, A. G., & Alsharif, A.M. Novel computations of the time-fractional Fisher’s model via generalized fractional integral operators by means of the Elzaki transform. Fractal and Fractional, 5(3), 94, (2021).
• Losada, J., & Nieto, J.J. Properties of a new fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 87-92, (2015).