Modeling of fractional-order COVID-19 epidemic model with quarantine and social distancing
Muhammad Farman
Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
Search for more papers by this authorMuhammad Aslam
Key Laboratory and Natural Functional Molecule Chemistry of Ministry of Education, Department of Chemistry and Materials Science, Northwest University, Xi'an, China
Search for more papers by this authorCorresponding Author
Ali Akgül
Art and Science Faculty, Department of Mathematics, Siirt University, Siirt, Turkey
Correspondence
Ali Akgül, Art and Science Faculty, Department of Mathematics, Siirt University, Siirt, Turkey.
Email: [email protected]
Communicated by: M. Efendiev
Search for more papers by this authorAqeel Ahmad
Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
Search for more papers by this authorMuhammad Farman
Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
Search for more papers by this authorMuhammad Aslam
Key Laboratory and Natural Functional Molecule Chemistry of Ministry of Education, Department of Chemistry and Materials Science, Northwest University, Xi'an, China
Search for more papers by this authorCorresponding Author
Ali Akgül
Art and Science Faculty, Department of Mathematics, Siirt University, Siirt, Turkey
Correspondence
Ali Akgül, Art and Science Faculty, Department of Mathematics, Siirt University, Siirt, Turkey.
Email: [email protected]
Communicated by: M. Efendiev
Search for more papers by this authorAqeel Ahmad
Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
Search for more papers by this authorAbstract
Different countries of the world are facing a serious pandemic of corona virus disease (COVID-19). One of the most typical treatments for COVID-19 is social distancing, which includes lockdown; it will help to decrease the number of contacts for undiagnosed individuals. The main aim of this article is to construct and evaluate a fractional-order COVID-19 epidemic model with quarantine and social distancing. Laplace homotopy analysis method is used for a system of fractional differential equation (FDEs) with Caputo and Atangana–Baleanu–Caputo (ABC) fractional derivative. By applying the ABC and Caputo derivative, the numerical solution for fractional-order COVID-19 epidemic model is achieved. The uniqueness and existence of the solution is checked by Picard–Lindelof's method. The proposed fractional model is demonstrated by numerical simulation which is useful for the government to control the spread of disease in a practical way.
FUNDING
There are no funders to report for this submission.
CONFLICT OF INTEREST
This work does not have any conflicts of interest.
REFERENCES
- 1Abubakar S, Akinwande NI, Abdulrahman S. A mathematical model of yellow fever epidemics. Afrika Mathematika. 2012; 6: 56-58.
- 2Hethcote HW. The mathematics of infectious diseases. Society for Industrial and Applied Mathematics, SIAM Rev. 2000; 42(4): 599-653.
- 3Baric RS, Fu K, Chen W, Yount B. High recombination and mutation rates in mouse hepatitis virus suggest that coronaviruses may be potentially important emerging viruses. Adv Experiment Med Biol. 1995; 380: 571-6.
- 4Weiss SR, Leibowitz JL. Coronavirus pathogenesis. Adv Virus Res. 2011; 81: 85-164.
- 5Su S, Wong G, Shi W, et al. Epidemiology, genetic recombination, and pathogenesis of coronaviruses. Trends Microbiol. 2016; 24: 490-502.
- 6Zhong NS, Zheng BJ, Li YM, et al. Epidemiology and cause of severe acute respiratory syndrome (SARS) in Guangdong, People's Republic of China, in February, 2003. Lancet. 2003; 362: 1353-8.
- 7Rivers C, Chretien JP, Riley S, et al. Using outbreak science to strengthen the use of models during epidemics. Nat Commun. 2019; 10: 3102.
- 8Linton MN, Kobayashi T, Yang Y. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data. J Clin Med. 2020; 9(2): 538.
- 9Huang C, Wang Y, Li X, et al. Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. Lancet. 2020; 395: 497-506.
- 10Bushnaq S, Khan SA, Shah K, Zaman G. Mathematical analysis of HIV/AIDS infection model with Caputo–Fabrizio fractional derivative. Cogent Math Stat. 2018; 5:1432521.
- 11Losada J, Nieto JJ. Properties of a new fractional derivative without singular kernel. Progress Fract Differ Appl. 2015; 1: 8792.
- 12 Caputo, Fabrizio M. A new definition of fractional derivative without singular kernel. Progr Fract Differ Appl. 2015; 1: 73-85.
- 13Alshabanat A, Jleli M, Kumar S, Samet B. Generalization of Caputo–Fabrizio fractional derivative and applications to electrical circuits. Front Phys. 2020; 8: 64.
- 14Kumar S, Ghosh S, Lotayif MSM, Samet B. A model for describing the velocity of a particle in Brownian motion by Robotnov function based fractional operator. Alexand Eng J. 2020; 59(3): 1435-1449.
- 15Veeresha P, Prakasha D. G., Kumar S. A fractional model for propagation of classical optical solitons by using nonsingular derivative. Math Methods Appl Sci. 2020. https://doi.org/10.1002/mma.6335
- 16Kumar S, Ghosh S, Samet B, Goufo EFD. An analysis for heat equations arises in diffusion process using new Yang Abdel Aty Cattani fractional operator. Math Methods Appl Sci. 2020; 43(9): 6062-6080.
- 17Saleem M, Farman M, Ahmad MO, Rizwan M. A control of artificial human pancreas. Chines J Phys. 2017; 55(6): 2273-2282.
- 18Farman M, Saleem MU, Ahmad A, Ahmad MO. Analysis and numerical solution of SEIR epidemic model of measles with non-integer time fractional derivatives by using Laplace Adomian decomposition method. Ain Shams Eng J. 2018; 9(4): 3391-3397.
- 19Farman M, Saleem MU, Ahmad M, Ahmad A. Stability analysis and control of glucose insulin glucagon system in human. Chines J Phys. 2018; 56: 1362-1369.
- 20Saleem M, Farman M, Rizwan M, Ahmad MO, Ahmad A. Controllability and observability of glucose insulin glucagon systems in human. Chines J Phys. 2018; 56(5): 1909-1916.
- 21Farman M, Saleem MU, Tabassum M, Ahmad A, Ahmad MO. A linear control of composite model for glucose insulin glucagon. Ain Shamas Eng J. 2019; 10: 867-872.
- 22Farman M, Ahmad A, Akgül A, Imtiaz S. Analysis and dynamical behavior of fractional order cancer model with vaccine strategy. Math Method Appl Sci. 2020; 43(7): 4871-4882. https://doi.org/10.1002/mma.6240
- 23Saleem MU, Farman M, Ahmad A, Ehsan H, Ahmad M. A caputo fabrizio fractional order model for control of glucose in insulin therapies for diabetes. Ain Shamas Eng J. 2020; 11(4): 1309-1316.
- 24Farman M, Saleem MU, Ahmad A, et al. A Control of Glucose Level in Insulin Therapies for the Development of Artificial Pancreas by Atangana Baleanu Fractional Derivative. Alexandria Eng J. 2020; 59: 2639-2648.
- 25Farman M, Akgül A, Baleanu D, Imtiaz S, Ahmad A. Analysis of fractional order chaotic financial model with minimum interest rate impact. Fractal Fract. 2020; 4: 43.
- 26Azhar H, Dumitru B, Saman Y. On a nonlinear fractional-order model of novel coronavirus (NCOV-2019) under AB-fractional derivative. To appear; 2020.
- 27Lin Q, Zhao S, Gao D, et al. A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individ- ual reaction and governmental action. Int J Infect Dis. 2020; 93: 211-16.
- 28Khan MA, Atangana A. Modeling the dynamics of novel coronavirus (2019- NCOV) with fractional derivative. Alexandria Eng J. 2020; 59(4): 2379-2389. https://doi.org/10.1016/j.aej.2020.02.033
- 29Redhwan SS, Abdob MS, Shah K, et al. Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator. Results Phys. 2020; 19:103610. https://doi.org/10.1016/j.rinp.2020.103610
- 30Fatima B, Zaman G, Alqudah MA, Abdeljawad T. Modeling the pandemic trend of 2019 Coronavirus with optimal control analysis. Results Phys. 2021; 20:103660. https://doi.org/10.1016/j.rinp.2020.103660
- 31Din RU, Shah K, Ahmad I, Abdeljawad T. Study of transmission dynamics of novel COVID-19 by using mathematical model. Adv Differ Equ. 2020; 2020: 323. https://doi.org/10.1186/s13662-020-02783-x
- 32Shah K, Abdeljawad T, Mahariq I, Jarad F. Qualitative analysis of a mathematical model in the time of COVID-19. BioMed Res Int. 2020; 2020:5098598. https://doi.org/10.1155/2020/5098598
- 33Yousef A, Bozkurt F, Abdeljawad T. Qualitative analysis of a fractional pandemic spread model of the novel coronavirus (COVID-19). Comput Materials Continua. 2021; 66(1): 843-869. https://doi.org/10.32604/cmc.2020.012060
- 34Bozkurt F, Yousef A, Abdeljawad T. Analysis of the Outbreak of the Novel Coronavirus COVID-19 Dynamic Model with Control Mechanisms. Results Phys. 2020; 19:103586. https://doi.org/10.1016/j.rinp.2020.103586
- 35Akgül A. A novel method for a fractional derivative with non-local and non-singular kernel. Chaos Solitons Fractals. 2018; 114: 478-482.
- 36Akgül EK. Solutions of the linear and nonlinear differential equations within the generalized fractional derivatives. Chaos. 2019; 29: 23108.
- 37Atangana A, Akgül A. Analysis and Applications of the New Derivative, Chapter of Fractional Order Analysis: Theory, Methods and Applications. John Wiley & Sons, Inc.; 2020: 91-111.
- 38Fernandez A, Baleanu D, Srivastava HM. Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions. Commun Nonlin Sci Numer Simul. 2019; 67: 517-527.
- 39MoralesDelgadoa VF, Aguilarb JF, Taneco MA, Escobar RF. Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel. J Nonlinear Sci Appl. 2018; 11: 994-1014.
10.22436/jnsa.011.08.06 Google Scholar
- 40Atangana A, Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. Therm Sci. 2016; 20: 763-769.
- 41Jafari H, Das S, Tajadodi H. Solving a multi-order fractional differential equation using homotopy analysis method. J King Saud Univ, Sci. 2011; 23(2): 151-155.
10.1016/j.jksus.2010.06.023 Google Scholar
- 42Morales VF, Gomez-Aguilar JF. Et all, Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular. Adv Differ Equ. 2016; 2016: 164.
- 43Kuniya T, Inaba H. Possible effects of mixed prevention strategy for COVID-19 epidemic: Massive testing, quarantine and social distancing. AIMS Public Health. 2020; 7(3): 490-503.
