Mathematical Modeling and Analysis for COVID-19 Model by Using Implicit-Explicit Rung-Kutta Methods
DOI:
https://doi.org/10.25007/ajnu.v11n3a1244Abstract
One of the most common health care problems globally is COVID-19, and also there are an international effort to monitor it have been proposed and discussed. Despite the fact that many studies have been performed based on clinical evidence and confirmed infected cases. However, there is room for additional research since a range of complex criteria are included for later research forecast. As a consequence, mathematical modelling mixed with the numerical simulations is an effective method for estimating main propagation parameters and forecasting disease model dynamics. We study and present some models for the COVID-19 in this paper, which can answer significant questions concerning global health care and implement important notes. The IMEX Runge–Kutta and classical Runge–Kutta methods are two well-known computational schemes to find the solution for such system of differential equations. The results, which are based on these numerical procedures suggested and provide estimated solutions, provide critical answers to this global problem. The amount of recovered, infected, susceptible, and quarantined people in the expectation can be estimated using numerical data. The findings could also aid international efforts to increase prevention and strengthen intervention programs. The findings could also support international efforts to increase prevention and strengthen intervention programs. It is clearly that the proposed methods more accurate and works in a very large interval in time with a few step sizes. That is consequently beginning to a decrease in the computational price of the method. Numerical experiments show that there is a good argument and accurate solutions for solving this type of problem.
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A. Ahmed, B. Salam, M. Mohammad, A. Akgul, and S. H. Khoshnaw, "Analysis coronavirus disease (COVID-19) model using numerical approaches and logistic model," Aims Bioengineering, vol. 7, no. 3, pp. 130-146, 2020.
S. He, S. Tang, and L. Rong, "A discrete stochastic model of the COVID-19 outbreak: Forecast and control," Math. Biosci. Eng, vol. 17, no. 4, pp. 2792-2804, 2020.
Q. Liu et al., "Assessing the global tendency of COVID-19 outbreak," MedRXiv, 2020.
B. Rahman, I. A. Aziz, F. W. Khdhr, and D. F. Mahmood, "Preliminary estimation of the basic reproduction number of SARS-CoV-2 in the Middle East," DOI: http://dx. doi. org/10.2471/BLT, vol. 20, 2020.
W. H. Organization, "Novel Coronavirus ( 2019-nCoV): situation report, 83," Available from: https://apps.who.int/iris/handle/10665/331781, 2020.
W. H. Organization, "Novel Coronavirus ( 2019-nCoV): situation report, 131," World Health Organization, 2020. Available from: https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200530-covid-19-sitrep-131.pdf?sfvrsn=d31ba4b3_2, 2020.
J. Cheng et al., "A novel electrochemical sensing platform for detection of dopamine based on gold nanobipyramid/multi-walled carbon nanotube hybrids," Analytical and bioanalytical chemistry, pp. 1-9, 2020.
C. Yang and J. Wang, "A mathematical model for the novel coronavirus epidemic in Wuhan, China," Mathematical biosciences and engineering: MBE, vol. 17, no. 3, p. 2708, 2020.
M. Mandal, S. Jana, S. K. Nandi, A. Khatua, S. Adak, and T. Kar, "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, vol. 136, p. 109889, 2020.
R. F. Reis et al., "Characterization of the COVID-19 pandemic and the impact of uncertainties, mitigation strategies, and underreporting of cases in South Korea, Italy, and Brazil," Chaos, Solitons & Fractals, vol. 136, p. 109888, 2020.
V. K. R. Chimmula and L. Zhang, "Time series forecasting of COVID-19 transmission in Canada using LSTM networks," Chaos, Solitons & Fractals, vol. 135, p. 109864, 2020.
M. S. Abdo, K. Shah, H. A. Wahash, and S. K. Panchal, "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, vol. 135, p. 109867, 2020.
M. H. D. M. Ribeiro, R. G. da Silva, V. C. Mariani, and L. dos Santos Coelho, "Short-term forecasting COVID-19 cumulative confirmed cases: Perspectives for Brazil," Chaos, Solitons & Fractals, vol. 135, p. 109853, 2020.
S. Boccaletti, W. Ditto, G. Mindlin, and A. Atangana, "Modeling and forecasting of epidemic spreading: The case of Covid-19 and beyond," Chaos, solitons, and fractals, vol. 135, p. 109794, 2020.
T. Chakraborty and I. Ghosh, "Real-time forecasts and risk assessment of novel coronavirus (COVID-19) cases: A data-driven analysis," Chaos, Solitons & Fractals, vol. 135, p. 109850, 2020.
J. Riou and C. L. Althaus, "Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020," Eurosurveillance, vol. 25, no. 4, p. 2000058, 2020.
B. Tang et al., "Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions," Journal of clinical medicine, vol. 9, no. 2, p. 462, 2020.
M. A. Khan and A. Atangana, "Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative," Alexandria Engineering Journal, vol. 59, no. 4, pp. 2379-2389, 2020.
T.-M. Chen, J. Rui, Q.-P. Wang, Z.-Y. Zhao, J.-A. Cui, and L. Yin, "A mathematical model for simulating the phase-based transmissibility of a novel coronavirus," Infectious diseases of poverty, vol. 9, no. 1, pp. 1-8, 2020.
A. J. Kucharski et al., "Early dynamics of transmission and control of COVID-19: a mathematical modelling study," The lancet infectious diseases, vol. 20, no. 5, pp. 553-558, 2020.
L. q. Li et al., "COVID‐19 patients' clinical characteristics, discharge rate, and fatality rate of meta‐analysis," Journal of medical virology, vol. 92, no. 6, pp. 577-583, 2020.
B. Tang, N. L. Bragazzi, Q. Li, S. Tang, Y. Xiao, and J. Wu, "An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov)," Infectious disease modelling, vol. 5, pp. 248-255, 2020.
K. Atkinson, W. Han, and D. E. Stewart, Numerical solution of ordinary differential equations. John Wiley & Sons, 2011.
D. Griffiths, "Higham. DJ: Numerical Methods for Ordinary Differential Equations," ed: Springer, 2010.
M. A. Islam, "A comparative study on numerical solutions of initial value problems (IVP) for ordinary differential equations (ODE) with Euler and Runge Kutta Methods," American Journal of computational mathematics, vol. 5, no. 03, p. 393, 2015.
L. Lapidus and J. H. Seinfeld, Numerical solution of ordinary differential equations. Academic press, 1971.
S. A. Manaa, M. A. Moheemmeed, and Y. A. Hussien, "A Numerical Solution for Sine-Gordon Type System," Tikrit Journal of Pure Science, vol. 15, no. 3, 2010.
R. C. Martins and N. Fachada, "Finite Element Procedures for Enzyme, Chemical Reaction and'In-Silico'Genome Scale Networks," arXiv preprint arXiv:1508.02506, 2015.
Y. A. Sabawi, "A Posteriori $ L_ {infty}(H^{1}) $ Error Bound in Finite Element Approximation of Semdiscrete Semilinear Parabolic Problems," in 2019 First International Conference of Computer and Applied Sciences (CAS), 2019, pp. 102-106: IEEE.
Y. A. Sabawi, "A Posteriori Error Analysis in Finite Element Approximation for Fully Discrete Semilinear Parabolic Problems," in Finite Element Methods and Their Applications: IntechOpen, 2020.
Y. A. Sabawi, "A Posteriori L_∞(L_2)+ L_2 (H^ 1)–Error Bounds in Discontinuous Galerkin Methods For Semidiscrete Semilinear Parabolic Interface Problems," Baghdad Science Journal, vol. 18, no. 3, pp. 0522-0522, 2021.
U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, "Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations," Applied Numerical Mathematics, vol. 25, no. 2-3, pp. 151-167, 1997.
L. Pareschi and G. Russo, "Implicit–explicit Runge–Kutta schemes and applications to hyperbolic systems with relaxation," Journal of Scientific computing, vol. 25, no. 1, pp. 129-155, 2005.
S. H. Khoshnaw, R. H. Salih, and S. Sulaimany, "Mathematical modelling for coronavirus disease (COVID-19) in predicting future behaviours and sensitivity analysis," Mathematical Modelling of Natural Phenomena, vol. 15, p. 33, 2020.
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