A new dynamical modeling SEIR with global analysis applied to the real data of spreading COVID-19 in Saudi Arabia

Hamdy M. Youssef; Najat A. Alghamdi; Magdy A. Ezzat; Alaa A. El-Bary; Ahmed M. Shawky; Hamdy M. Youssef; Najat A. Alghamdi; Magdy A. Ezzat; Alaa A. El-Bary; Ahmed M. Shawky

doi:10.3934/mbe.2020362

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7018-7044. doi: 10.3934/mbe.2020362

Previous Article Next Article

Research article

A new dynamical modeling SEIR with global analysis applied to the real data of spreading COVID-19 in Saudi Arabia

1.
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, Saudi Arabia
2.
Department of Mathematics, Faculty of Applied Science, Umm Al-Qura University, Makkah, Saudi Arabia
3.
College of Science and Arts, Al-Qassim University, Al Bukairiyah, Al Qassim, Saudi Arabia
4.
Basic and Applied Science Institute, Arab Academy for Science, Technology, and Maritime Transport, Alexandria, Egypt
5.
Science and Technology Unit (STU), Umm Al-Qura University, Makkah, Saudi Arabia

Received: 14 July 2020 Accepted: 13 October 2020 Published: 16 October 2020

SEIR model is a widely used and acceptable model to distinguish the outbreak of the COVID-19 epidemic in many countries. In the current work, a new proposed SEIR model as a mathematical model for the outbreak of novel coronaviruses COVID-19 will be constructed. The new proposed SEIR pandemic model provides a new vision for evaluations and management of the epidemic of COVID-19 infection. For mathematical modeling and dynamic analyses, this paper uses the real data of spreading COVID-19 in Saudi Arabia. The dynamics of the proposed SEIR model are presented with the reproduction number and the extensive stability analysis. We discussed the domain of the solution and equilibrium situation based on the proposed SEIR model by using Jacobian's method of linearization. The condition of equilibrium and its uniqueness has been proved, and the stability analysis of disease-free equilibrium has been introduced. A sensitivity analysis of the reproduction number against its internal parameters has been done. The global stability of the equilibrium of this model has been proved by using Lyapunov's Stability theorem. A numerical verification and predictions of the proposed SEIR model have been made with comparing the results based on the SEIR model and the real data due to the spreading of the COVID-19 in Saudi Arabia. The proposed SEIR model is a successful model to analyze the spreading of epidemics like COVID-19. This work introduces the ideal protocol, which can help the Saudi population to breakdown spreading COVID-19 in a fast way.
- novel coronavirus,
- COVID-19,
- SEIR model,
- Jacobian matrix,
- reproduction number,
- Lyapunov's stability
Citation: Hamdy M. Youssef, Najat A. Alghamdi, Magdy A. Ezzat, Alaa A. El-Bary, Ahmed M. Shawky. A new dynamical modeling SEIR with global analysis applied to the real data of spreading COVID-19 in Saudi Arabia[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7018-7044. doi: 10.3934/mbe.2020362

Related Papers:

Abstract

SEIR model is a widely used and acceptable model to distinguish the outbreak of the COVID-19 epidemic in many countries. In the current work, a new proposed SEIR model as a mathematical model for the outbreak of novel coronaviruses COVID-19 will be constructed. The new proposed SEIR pandemic model provides a new vision for evaluations and management of the epidemic of COVID-19 infection. For mathematical modeling and dynamic analyses, this paper uses the real data of spreading COVID-19 in Saudi Arabia. The dynamics of the proposed SEIR model are presented with the reproduction number and the extensive stability analysis. We discussed the domain of the solution and equilibrium situation based on the proposed SEIR model by using Jacobian's method of linearization. The condition of equilibrium and its uniqueness has been proved, and the stability analysis of disease-free equilibrium has been introduced. A sensitivity analysis of the reproduction number against its internal parameters has been done. The global stability of the equilibrium of this model has been proved by using Lyapunov's Stability theorem. A numerical verification and predictions of the proposed SEIR model have been made with comparing the results based on the SEIR model and the real data due to the spreading of the COVID-19 in Saudi Arabia. The proposed SEIR model is a successful model to analyze the spreading of epidemics like COVID-19. This work introduces the ideal protocol, which can help the Saudi population to breakdown spreading COVID-19 in a fast way.

References

[1]	M. A. Khan, A. Atangana, Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative, Alexandria Eng. J., 59 (2020), 2379-2389. doi: 10.1016/j.aej.2020.02.033
[2]	H. Lu, C. W. Stratton, Y. W. Tang, Outbreak of Pneumonia of Unknown Etiology in Wuhan China: the Mystery and the Miracle, J. Med. Virol., 92 (2020), 401-402. doi: 10.1002/jmv.25678
[3]	M. Goyal, H. M. Baskonus, A. Prakash, An efficient technique for a time fractional model of lassa hemorrhagic fever spreading in pregnant women, Eur. Phys. J. Plus, 134 (2019), 482. doi: 10.1140/epjp/i2019-12854-0
[4]	W. Gao, P. Veeresha, D. Prakasha, H. M. Baskonus, G. Ye, New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function, Chaos, Solitons Fractals, 134 (2020), 109696. doi: 10.1016/j.chaos.2020.109696
[5]	D. Kumar, J. Singh, M. Al Qurashi, D. Baleanu, A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying, Adv. Differ. Equations, 2019 (2019), 278.
[6]	K. Shah, M. A. Alqudah, F. Jarad, T. Abdeljawad, Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo-Febrizio fractional order derivative, Chaos, Solitons Fractals, 135 (2020), 109754. doi: 10.1016/j.chaos.2020.109754
[7]	M. Martcheva, An introduction to mathematical epidemiology, Springer, 2015.
[8]	P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6
[9]	J. T. Wu, K. Leung, G. M. Leung, Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study, Lancet, 395 (2020), 689-697.
[10]	J. M. Read, J. R. Bridgen, D. A. Cummings, A. Ho, C. P. Jewell, Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions, Fourthcoming 2020.
[11]	B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Tang, Y. Xiao, et al., Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions, J. Clin. Med., 9 (2020), 462. doi: 10.3390/jcm9020462
[12]	N. Imai, A. Cori, I. Dorigatti, M. Baguelin, C. A. Donnelly, S. Riley, et al., Report 3: transmissibility of 2019-nCoV, Imperial College London, 2020. Available from: https://doi.org/10.25561/77148.
[13]	H. Zhu, Q. Guo, M. Li, C. Wang, Z. Fang, P. Wang, et al., Host and infectivity prediction of Wuhan 2019 novel coronavirus using deep learning algorithm, Fourthcoming 2020.
[14]	C. Yang, J. Wang, A mathematical model for the novel coronavirus epidemic in Wuhan, China, Math. Biosci. Eng., 17 (2020), 2708-2724. doi: 10.3934/mbe.2020148
[15]	K. Wang, Z. Lu, X. Wang, H. Li, Z. Peng, Current trends and future prediction of novel coronavirus disease (COVID-19) epidemic in China: a dynamical modeling analysis, Math. Biosci. Eng., 17 (2020), 3052-3061. doi: 10.3934/mbe.2020173
[16]	R. U. Din, K. Shah, I. Ahmad, T. Abdeljawad, Study of Transmission Dynamics of Novel COVID-19 by Using Mathematical Model, Adv. Differ. Equation, 2020 (2020).
[17]	L. Peng, W. Yang, D. Zhang, C. Zhuge, L. Hong, Epidemic analysis of COVID-19 in China by dynamical modeling, Forthcoming 2020.
[18]	J. F. Rabajante, Insights from early mathematical models of 2019-nCoV acute respiratory disease (COVID-19) dynamics, Forthcoming 2020.
[19]	L. Mangoni, M. Pistilli, Epidemic analysis of Covid-19 in Italy by dynamical modelling, SSRN Electron. J., 2020 (2020).
[20]	S. S. Nadim, I. Ghosh, J. Chattopadhyay, Short-term predictions and prevention strategies for COVID-2019: A model based study, Forthcoming 2020.
[21]	A. J. Kucharski, T. W. Russell, C. Diamond, et al., Early dynamics of transmission and control of COVID-19: a mathematical modelling study, Lancet Infect Dis., 20 (2020), 553-558. doi: 10.1016/S1473-3099(20)30144-4
[22]	T. Chen, J. Rui, Q. Wang, Z. Zhao, J. A. Cui, L. Yin, A mathematical model for simulating the transmission of Wuhan novel Coronavirus, Forthcoming 2020.
[23]	D. Benvenuto, M. Giovanetti, L. Vassallo, S. Angeletti, M. Ciccozzi, Application of the ARIMA model on the COVID-2019 epidemic dataset, Data Brief, 29 (2020), 105340. doi: 10.1016/j.dib.2020.105340
[24]	M. De la Sen, R. P. Agarwal, A. Ibeas, S. Alonso-Quesada, On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls, Adv. Differ. Equations, 2010 (2010), 281612. doi: 10.1186/1687-1847-2010-281612
[25]	X. Song, Y. Jiang, H. Wei, Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays, Appl. Math. Comput.n, 214 (2009), 381-390. doi: 10.1016/j.amc.2009.04.005
[26]	D. Pal, D. Ghosh, P. Santra, G. S. Mahapatra, Mathematical Analysis of a COVID-19 Epidemic Model by using Data Driven Epidemiological Parameters of Diseases Spread in India, Forthcoming 2020.
[27]	Minisry of Health, https://www.moh.gov.sa/en/Pages/default.aspx, (2020).
[28]	COVID-19 pandemic in Saudi Arabia, https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Saudi_Arabia, (2020).
[29]	Saudi Center for Deasies Preventation and Control, https://covid19.cdc.gov.sa/ar/daily-updates-ar/, (2020).

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)