### AIMS Bioengineering

2020, Issue 3: 130-146. doi: 10.3934/bioeng.2020013
Research Article Special Issues

# Analysis coronavirus disease (COVID-19) model using numerical approaches and logistic model

• Received: 13 May 2020 Accepted: 05 June 2020 Published: 18 June 2020
• The coronavirus disease (COVID-19) is a global health care problem that international efforts have been suggested and discussed to control this disease. Although, there are many researches have been conducted on the basis of the clinical data and recorded infected cases, there is still scope for further research due to the fact that a number of complicated parameters are involved for future prediction. Thus, mathematical modeling with computational simulations is an important tool that estimates key transmission parameters and predicts model dynamics of the disease. In this paper, we review and introduce some models for the COVID-19 that can address important questions about the global health care and suggest important notes. We suggest three well known numerical techniques for solving such equations, they are Euler's method, Runge–Kutta method of order two (RK2) and of order four (RK4). Results based on the suggested numerical techniques and providing approximate solutions give important key answers to this global issue. Numerical results may use to estimate the number susceptible, infected, recovered and quarantined individuals in the future. The results here may also help international efforts for more preventions and improvement their intervention programs. More interestedly, for both countries, Turkey and Iraq, the basic reproduction numbers R0 have been reported recently by several groups, a research estimation by 9 April 2020 revealed that R0 for Turkey is 7.4 and for Iraq is 3.4, which are noticeably increased from the beginning of the pandemic. In addition, on the basis of WHO situation reports, the new confirmed cases in Turkey on 11 April are 5138, and in Iraq on 29 May are 416, which can be counted as the peak value from the beginning of the disease. Thus, we investigate the forecasting epidemic size for Turkey and Iraq using the logistic model. It can be concluded that the suggested model is a reasonable description of this epidemic disease.

Citation: Ayub Ahmed, Bashdar Salam, Mahmud Mohammad, Ali Akgül, Sarbaz H. A. Khoshnaw. Analysis coronavirus disease (COVID-19) model using numerical approaches and logistic model[J]. AIMS Bioengineering, 2020, 7(3): 130-146. doi: 10.3934/bioeng.2020013

### Related Papers:

• The coronavirus disease (COVID-19) is a global health care problem that international efforts have been suggested and discussed to control this disease. Although, there are many researches have been conducted on the basis of the clinical data and recorded infected cases, there is still scope for further research due to the fact that a number of complicated parameters are involved for future prediction. Thus, mathematical modeling with computational simulations is an important tool that estimates key transmission parameters and predicts model dynamics of the disease. In this paper, we review and introduce some models for the COVID-19 that can address important questions about the global health care and suggest important notes. We suggest three well known numerical techniques for solving such equations, they are Euler's method, Runge–Kutta method of order two (RK2) and of order four (RK4). Results based on the suggested numerical techniques and providing approximate solutions give important key answers to this global issue. Numerical results may use to estimate the number susceptible, infected, recovered and quarantined individuals in the future. The results here may also help international efforts for more preventions and improvement their intervention programs. More interestedly, for both countries, Turkey and Iraq, the basic reproduction numbers R0 have been reported recently by several groups, a research estimation by 9 April 2020 revealed that R0 for Turkey is 7.4 and for Iraq is 3.4, which are noticeably increased from the beginning of the pandemic. In addition, on the basis of WHO situation reports, the new confirmed cases in Turkey on 11 April are 5138, and in Iraq on 29 May are 416, which can be counted as the peak value from the beginning of the disease. Thus, we investigate the forecasting epidemic size for Turkey and Iraq using the logistic model. It can be concluded that the suggested model is a reasonable description of this epidemic disease.

Conflict of interest

The authors declare that there are no competing interests.

 [1] He S, Tang S, Rong L (2020) A discrete stochastic model of the COVID-19 outbreak: forecast and control. Math Biosci Eng 17: 2792-2804. doi: 10.3934/mbe.2020153 [2] Rahman B, Aziz IA, Khdhr FW, et al. (2020)  Preliminary estimation of the basic reproduction number of SARS-CoV-2 in the Middle East. doi: 10.2471/BLT.20.262295 [3] Liu Q, Liu Z, Zhu J, et al. (2020)  Assessing the global tendency of COVID-19 outbreak. doi: 10.1101/2020.03.18.20038224 [4] World Health Organization, Novel coronavirus (2019-nCoV) situation report 83, 2020. Available from: https://apps.who.int/iris/handle/10665/331781. [5] World Health Organization (2020)  WHO, Novel coronavirus (2019-nCoV) situation report 131. Available from: https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200530-covid-19-sitrep-131.pdf?sfvrsn=d31ba4b3_2. [6] Cheng J, Wang X, Nie T, et al. (2020) A novel electrochemical sensing platform for detection of dopamine based on gold nanobipyramid/multi-walled carbon nanotube hybrids. Ana Bioanal Chem 412: 2433-2441. doi: 10.1007/s00216-020-02455-5 [7] Yang C, Wang J (2020) A mathematical model for the novel coronavirus epidemic in Wuhan, China. Math Biosci Eng 17: 2708-2724. doi: 10.3934/mbe.2020148 [8] Mandal M, Jana S, Nandi SK, et al. (2020) A model based study on the dynamics of COVID-19: prediction and control. Chaos Soliton Fract 136: 109889. doi: 10.1016/j.chaos.2020.109889 [9] Reis RF, de Melo Quintela B, de Oliveira Campos J, et al. (2020) Characterization of the COVID-19 pandemic and the impact of uncertainties, mitigation strategies, and underreporting of cases in South Korea, Italy, and Brazil. Chaos Soliton Fract 136: 109888. doi: 10.1016/j.chaos.2020.109888 [10] Chimmula VKR, Zhang L (2020) Time series forecasting of COVID-19 transmission in canada using LSTM networks. Chaos Soliton Fract 135: 109864. doi: 10.1016/j.chaos.2020.109864 [11] Abdo MS, Shah K, Wahash HA, et al. (2020) On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative. Chaos Soliton Fract 135: 109867. doi: 10.1016/j.chaos.2020.109867 [12] Ribeiro MHDM, da Silva RG, Mariani VC, et al. (2020) Short-term forecasting COVID-19 cumulative confirmed cases: perspectives for Brazil. Chaos Soliton Fract 135: 109853. doi: 10.1016/j.chaos.2020.109853 [13] Boccaletti S, Ditto W, Mindlin G, et al. (2020) Modeling and forecasting of epidemic spreading: The case of Covid-19 and beyond. Chaos Soliton Fract 135: 109794. doi: 10.1016/j.chaos.2020.109794 [14] Chakraborty T, Ghosh I (2020) Real-time forecasts and risk assessment of novel coronavirus (COVID-19) cases: a data-driven analysis. Chaos Soliton Fract 135: 109850. doi: 10.1016/j.chaos.2020.109850 [15] Riou J, Althaus CL (2020) Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020. Eurosurveillance 25: 2000058. doi: 10.2807/1560-7917.ES.2020.25.4.2000058 [16] Tang B, Wang X, Li Q, et al. (2020) Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions. J Clin Med 9: 462. doi: 10.3390/jcm9020462 [17] Khan MA, Atangana A (2020)  Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. doi: 10.1016/j.aej.2020.02.033 [18] Kucharsk AJ, Russell TW, Diamond C, et al. (2020) Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect Dis 20: 553-558. doi: 10.1016/S1473-3099(20)30144-4 [19] Chen TM, Rui J, Wang QP, et al. (2020) A mathematical model for simulating the phase-based transmissibility of a novel coronavirus. Infect Dis Poverty 9: 24. doi: 10.1186/s40249-020-00640-3 [20] Tang B, Bragazzi NL, Li Q, et al. (2020) An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infect Dis Model 5: 248-255. [21] Li LQ, Huang T, Wang YQ, et al. (2020) COVID-19 patients' clinical characteristics, discharge rate, and fatality rate of meta-analysis. J Med Virol 92: 577-583. doi: 10.1002/jmv.25757 [22] Shawagfeh N, Kaya D (2004) Comparing numerical methods for the solutions of systems of ordinary differential equations. Appl Math Lett 17: 323-328. doi: 10.1016/S0893-9659(04)90070-5 [23] Burden RL, Faires JD (2011)  Numerical Analysis USA: Brooks/Cole, Cencag Learning. [24] Atkinson K, Han W, Stewart DE (2011)  Numerical Solution of Ordinary Differential Equations New Jersey: John Wiley & Sons. [25] Griffiths DF, Higham DJ (2010)  Numerical Methods for Ordinary Differential Equations: Initial Value Problems New York: Springer Science & Business Media. doi: 10.1007/978-0-85729-148-6 [26] King MR, Mody NA (2010)  Numerical and Statistical Methods for Bioengineering: Applications in MATLAB UK: Cambridge University Press. doi: 10.1017/CBO9780511780936 [27] Islam MA (2015) A comparative study on numerical solutions of initial value problems (IVP) for ordinary differential equations (ODE) with Euler and Runge Kutta Methods. Am J Comput Math 5: 393-404. doi: 10.4236/ajcm.2015.53034 [28] Fausett LV (1999)  Applied Numerical Analysis Using MATLAB New Jersey: Prentice hall. [29] Khoshnaw SHA (2015)  Model reductions in biochemical reaction networks [PhD thesis] UK: University of Leicester. [30] Akgül A, Khoshnaw SHA, Mohammed WH (2018) Mathematical model for the Ebola Virus Disease. J Adv Phys 7: 190-198. doi: 10.1166/jap.2018.1407 [31] Khoshnaw SHA (2019) A mathematical modelling approach for childhood vaccination with some computational simulations. AIP Conference Proceedings 2096: 020022. doi: 10.1063/1.5097819 [32] Khoshnaw SHA, Mohammad NA, Salih RH (2017) Identifying critical parameters in SIR model for spread of disease. Open J Model Simul 5: 73291. [33] Batista M (2020)  fitVirus, MATLAB Central File Exchange. Available from: https://www.mathworks.com/matlabcentral/fileexchange/74411-fitvirus. [34] Tuli S, Tuli S, Tuli R, et al. (2020) Predicting the growth and trend of COVID-19 pandemic using machine learning and cloud computing. Internet Things 11: 100222. doi: 10.1016/j.iot.2020.100222 [35] Khoshnaw SHA, Salih RH, Sulaimany S (2020) Mathematical modelling for coronavirus disease (COVID-19) in predicting future behaviours and sensitivity analysis. Math Model Nat Pheno 15: 33. doi: 10.1051/mmnp/2020020 [36] Khoshnaw SHA, Shahzad M, Ali M, et al. (2020) A quantitative and qualitative analysis of the COVID-19 pandemic model. Chaos Soliton Fract 109932. doi: 10.1016/j.chaos.2020.109932

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沈阳化工大学材料科学与工程学院 沈阳 110142

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