Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia

Salma M. Al-Tuwairqi; Sara K. Al-Harbi; Salma M. Al-Tuwairqi; Sara K. Al-Harbi

doi:10.3934/mbe.2022456

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 9792-9824. doi: 10.3934/mbe.2022456

Previous Article Next Article

Research article Special Issues

Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia

Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Academic Editor: Quentin Griette

Received: 20 May 2022 Revised: 16 June 2022 Accepted: 21 June 2022 Published: 08 July 2022

Saudi Arabia was among the countries that attempted to manage the COVID-19 pandemic by developing strategies to control the epidemic. Lockdown, social distancing and random diagnostic tests are among these strategies. In this study, we formulated a mathematical model to investigate the impact of employing random diagnostic tests to detect asymptomatic COVID-19 patients. The model has been examined qualitatively and numerically. Two equilibrium points were obtained: the COVID-19 free equilibrium and the COVID-19 endemic equilibrium. The local and global asymptotic stability of the equilibrium points depends on the control reproduction number $\mathcal{R}_{c}$ . The model was validated by employing the Saudi Ministry of Health COVID-19 dashboard data. Numerical simulations were conducted to substantiate the qualitative results. Further, sensitivity analysis was performed on $\mathcal{R}_{c}$ to scrutinize the significant parameters for combating COVID-19. Finally, different scenarios for implementing random diagnostic tests were explored numerically along with the control strategies applied in Saudi Arabia.

Keywords:

Citation: Salma M. Al-Tuwairqi, Sara K. Al-Harbi. Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 9792-9824. doi: 10.3934/mbe.2022456

Related Papers:

[1]	Yali Ouyang, Zhuhuang Zhou, Weiwei Wu, Jin Tian, Feng Xu, Shuicai Wu, Po-Hsiang Tsui . A review of ultrasound detection methods for breast microcalcification. Mathematical Biosciences and Engineering, 2019, 16(4): 1761-1785. doi: 10.3934/mbe.2019085
[2]	Qun Xia, Yangmei Cheng, Jinhua Hu, Juxia Huang, Yi Yu, Hongjuan Xie, Jun Wang . Differential diagnosis of breast cancer assisted by S-Detect artificial intelligence system. Mathematical Biosciences and Engineering, 2021, 18(4): 3680-3689. doi: 10.3934/mbe.2021184
[3]	Yue Zhang, Haitao Gan, Furong Wang, Xinyao Cheng, Xiaoyan Wu, Jiaxuan Yan, Zhi Yang, Ran Zhou . A self-supervised fusion network for carotid plaque ultrasound image classification. Mathematical Biosciences and Engineering, 2024, 21(2): 3110-3128. doi: 10.3934/mbe.2024138
[4]	Haiyan Song, Cuihong Liu, Shengnan Li, Peixiao Zhang . TS-GCN: A novel tumor segmentation method integrating transformer and GCN. Mathematical Biosciences and Engineering, 2023, 20(10): 18173-18190. doi: 10.3934/mbe.2023807
[5]	Xiaoyue Fang, Ran Zhou, Haitao Gan, Mingyue Ding, Ming Yuchi . Time-of-flight completion in ultrasound computed tomography based on the singular value threshold algorithm. Mathematical Biosciences and Engineering, 2022, 19(10): 10160-10175. doi: 10.3934/mbe.2022476
[6]	Salman Lari, Hossein Rajabzadeh, Mohammad Kohandel, Hyock Ju Kwon . A holistic physics-informed neural network solution for precise destruction of breast tumors using focused ultrasound on a realistic breast model. Mathematical Biosciences and Engineering, 2024, 21(10): 7337-7372. doi: 10.3934/mbe.2024323
[7]	Hong Yu, Wenhuan Lu, Qilong Sun, Haiqiang Shi, Jianguo Wei, Zhe Wang, Xiaoman Wang, Naixue Xiong . Design and analysis of a robust breast cancer diagnostic system based on multimode MR images. Mathematical Biosciences and Engineering, 2021, 18(4): 3578-3597. doi: 10.3934/mbe.2021180
[8]	Chenkai Chang, Fei Qi, Chang Xu, Yiwei Shen, Qingwu Li . A dual-modal dynamic contour-based method for cervical vascular ultrasound image instance segmentation. Mathematical Biosciences and Engineering, 2024, 21(1): 1038-1057. doi: 10.3934/mbe.2024043
[9]	Xiaochen Liu, Weidong He, Yinghui Zhang, Shixuan Yao, Ze Cui . Effect of dual-convolutional neural network model fusion for Aluminum profile surface defects classification and recognition. Mathematical Biosciences and Engineering, 2022, 19(1): 997-1025. doi: 10.3934/mbe.2022046
[10]	Jiajun Zhu, Rui Zhang, Haifei Zhang . An MRI brain tumor segmentation method based on improved U-Net. Mathematical Biosciences and Engineering, 2024, 21(1): 778-791. doi: 10.3934/mbe.2024033

Abstract

References

[1]	WHO Director-General's opening remarks at the media briefing on COVID-19 - 11 March 2020, 2020. Available from: https://www.who.int/director-general/speeches/detail.
[2]	Weekly epidemiological update on COVID-19 - 28 December 2021, 2021. Available from: https://www.who.int/publications/m/item/weekly-epidemiological-update-on-covid-19-28-december-2021.
[3]	Y. Wang, Y. Wang, Y. Chen, Q. Qin, Unique epidemiological and clinical features of the emerging 2019 novel coronavirus pneumonia (COVID-19) implicate special control measures, J. Med. Virol., 92 (2020), 568–576. https://doi.org/10.1002/jmv.25748 doi: 10.1002/jmv.25748
[4]	Z. Gao, Y. Xu, C. Sun, X. Wang, Y. Guo, S. Qiu, et al., A systematic review of asymptomatic infections with COVID-19. J. Microbiol. Immunol. Infect., 54 (2021), 12–16. https://doi.org/10.1016/j.jmii.2020.05.001 doi: 10.1016/j.jmii.2020.05.001
[5]	Y. Bai, L. Yao, T. Wei, F. Tian, D. Jin, L. Chen, et al., Presumed asymptomatic carrier transmission of COVID-19, Jama, 323 (2020), 1406–1407. https://doi.org/10.1001/jama.2020.2565 doi: 10.1001/jama.2020.2565
[6]	R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang, et al., Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2), Science, 368 (2020), 489–493. https://doi.org/10.1126/science.abb3221 doi: 10.1126/science.abb3221
[7]	G. Kim, M. Kim, S. Ra, J. Lee, S. Bae, J. Jung, et al., Clinical characteristics of asymptomatic and symptomatic patients with mild COVID-19, Clin. Microbiol. Infect., 26 (2020), 948.e1–948.e3. https://doi.org/10.1016/j.cmi.2020.04.040 doi: 10.1016/j.cmi.2020.04.040
[8]	J. M. AlJishi, A. H. Alhajjaj, F. L. Alkhabbaz, T. H. AlAbduljabar, A. Alsaif, H. Alsaif, et al., Clinical characteristics of asymptomatic and symptomatic COVID-19 patients in the eastern province of Saudi Arabia, J. Infect. Public Health, 14 (2021), 6–11. https://doi.org/10.1016/j.jiph.2020.11.002 doi: 10.1016/j.jiph.2020.11.002
[9]	Y. M. Alsofayan, S. M. Althunayyan, A. A. Khan, A. M. Hakawi, A. M. Assiri, Clinical characteristics of COVID-19 in Saudi Arabia: A national retrospective study, J. Infect. Public Health, 13 (2020), 920–925. https://doi.org/10.1016/j.jiph.2020.05.026 doi: 10.1016/j.jiph.2020.05.026
[10]	F. S. Alshammari, A mathematical model to investigate the transmission of COVID-19 in the kingdom of Saudi Arabia, Comput. Math. Methods. Med., 2020 (2020), 1–13. https://doi.org/10.1155/2020/9136157 doi: 10.1155/2020/9136157
[11]	I. Ahmed, G. U. Modu, A. Yusuf, P. Kumam, I. Yusuf, A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes, Results Phys., 21 (2021), 103776. https://doi.org/10.1016/j.rinp.2020.103776 doi: 10.1016/j.rinp.2020.103776
[12]	N. Anggriani, M. Z. Ndii, R. Amelia, W. Suryaningrat, M. A. A. Pratama, A mathematical COVID-19 model considering asymptomatic and symptomatic classes with waning immunity, Alexandria Eng. J., 61 (2022), 113–124. https://doi.org/10.1016/j.aej.2021.04.104 doi: 10.1016/j.aej.2021.04.104
[13]	E. Alzahrani, M. El-Dessoky, D. Baleanu, Mathematical modeling and analysis of the novel Coronavirus using Atangana–Baleanu derivative, Results Phys., 25 (2021), 104240. https://doi.org/10.1016/j.rinp.2021.104240 doi: 10.1016/j.rinp.2021.104240
[14]	M. S. Alqarni, M. Alghamdi, T. Muhammad, A. S. Alshomrani, M. A. Khan, Mathematical modeling for novel coronavirus (COVID-19) and control, Numer. Methods Partial. Differ. Equ., (2020), 1–17. https://doi.org/10.1002/num.22695
[15]	T. Sun, D. Weng, Estimating the effects of asymptomatic and imported patients on COVID-19 epidemic using mathematical modeling, J. Med. Virol., 92 (2020), 1995–2003. https://doi.org/10.1002/jmv.25939 doi: 10.1002/jmv.25939
[16]	M. Serhani, H. Labbardi, Mathematical modeling of COVID-19 spreading with asymptomatic infected and interacting peoples, J. Appl. Math. Comput., 66 (2021), 1–20. https://doi.org/10.1007/s12190-020-01421-9 doi: 10.1007/s12190-020-01421-9
[17]	X. Huo, J. Chen, S. Ruan, Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study, BMC infect. Dis., 21 (2021), 1–18. https://doi.org/10.1186/s12879-021-06078-8 doi: 10.1186/s12879-021-06078-8
[18]	N. Al-Salti, I. M. Elmojtaba, J. Mesquita, D. Pastore, M. Al-Yahyai, Mathematical Analysis of Diagnosis Rate Effects in Covid-19 Transmission Dynamics with Optimal Control, in Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact, Springer, (2021), 219–244. https://doi.org/10.1007/978-981-16-2450-6_11
[19]	D. Ibarra-Vega, Lockdown, one, two, none, or smart. Modeling containing COVID-19 infection. A conceptual model, Sci. Total Environ., 730 (2020), 138917. https://doi.org/10.1016/j.scitotenv.2020.138917 doi: 10.1016/j.scitotenv.2020.138917
[20]	S. Alrashed, N. Min-Allah, A. Saxena, I. Ali, R. Mehmood, Impact of lockdowns on the spread of COVID-19 in Saudi Arabia, Inform. Med. Unlocked., 20 (2020), 100420. https://doi.org/10.1016/j.imu.2020.100420 doi: 10.1016/j.imu.2020.100420
[21]	D. Fanelli and F. Piazza, Analysis and forecast of COVID-19 spreading in China, Italy and France, Chaos Solitons Fractals, 134 (2020), 109761. https://doi.org/10.1016/j.chaos.2020.109761 doi: 10.1016/j.chaos.2020.109761
[22]	D. Aldila, S. Khoshnaw, E. Safitri, Y. Anwar, A. Bakry, B. Samiadji, et al., A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia, Chaos Solitons Fractals, 139 (2020), 110042. https://doi.org/10.1016/j.chaos.2020.110042 doi: 10.1016/j.chaos.2020.110042
[23]	N. Ahmad, COVID-19 modeling in Saudi Arabia using the modified Susceptible-Exposed-Infectious-Recovered (SEIR) model, Cureus, 12 (2020), e10452. https://doi.org/10.7759/cureus.10452. doi: 10.7759/cureus.10452
[24]	S. Ullah, M. A. Khan, Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study, Chaos Solitons Fractals, 139 (2020), 110075. https://doi.org/10.1016/j.chaos.2020.110075 doi: 10.1016/j.chaos.2020.110075
[25]	S. M. Kassa, J. Njagarah, Y. A. Terefe, Analysis of the mitigation strategies for COVID-19: From mathematical modelling perspective, Chaos Solitons Fractals, 138 (2020), 109968. https://doi.org/10.1016/j.chaos.2020.109968 doi: 10.1016/j.chaos.2020.109968
[26]	Y. Ding, L. Gao, An evaluation of COVID-19 in Italy: A data-driven modeling analysis, Infectious Disease Modelling, 5 (2020), 495–501. https://doi.org/10.1016/j.idm.2020.06.007 doi: 10.1016/j.idm.2020.06.007
[27]	T. Phan, K. Nagaro, Diagnostic Tests for COVID-19, in Coronavirus Disease-COVID-19, Springer, (2021), 403–412. https://doi.org/10.1007/978-3-030-63761-3_23
[28]	A. Khan, H. Alahdal, R. Alotaibi, H. Sonbol, R. Almaghrabi, Y. Alsofayan, et al., Controlling COVID-19 pandemic: A mass screening experience in Saudi Arabia, Front. Public Health, 8 (2021), 1013. https://doi.org/10.3389/fpubh.2020.606385 doi: 10.3389/fpubh.2020.606385
[29]	Saudi Arabia's Experience in Health Preparedness and Response to COVID-19 Pandemic, 2020. Available from: https://www.moh.gov.sa/en/Ministry/MediaCenter/Publications/Pages/Publications-2020-10-27-001.aspx.
[30]	Active Surveillance Detects COVID-19 Cases in Makkah and Madinah, 2020. Available from: https://www.moh.gov.sa/en/Ministry/MediaCenter/News/Pages/News-2020-04-18-002.aspx.
[31]	MOH Announces Third Stage of Expanded COVID-19 Testing, 2020. Available from: https://www.moh.gov.sa/en/Ministry/MediaCenter/News/Pages/News-2020-05-19-006.aspx.
[32]	MOH: Third Stage of (Takkad) Initiative Centers Launched, 2020. Available from: https://www.moh.gov.sa/en/Ministry/MediaCenter/News/Pages/News-2020-06-17-004.aspx.
[33]	MOH Performs 200,000 Coronavirus PCR Testing, COVID-19 Monitoring Committee Says, 2020. Available from: https://www.moh.gov.sa/en/Ministry/MediaCenter/News/Pages/News-2020-04-21-005.aspx.
[34]	Over 600,000 Self-assessment Exams Throught "Mawid" App, COVID-19 Monitoring Committee Says, 2020. Available from: https://www.moh.gov.sa/en/Ministry/MediaCenter/News/Pages/News-2020-04-25-001.aspx.
[35]	Saudi Arabia Sings 955 Million SR Contract with China for Testing Coronavirus, 2020. Available from: https://www.spa.gov.sa/viewfullstory.php?lang=en&newsid=2079249.
[36]	MOH: Over 2M Beneficiaries of "Takkad" Centers and "Tetamman" Clinics, 2020. Available from: https://www.moh.gov.sa/en/Ministry/MediaCenter/News/Pages/News-2020-08-12-007.aspx.
[37]	S. K. Al-Harbi, S. M. Al-Tuwairqi, Modeling the effect of lockdown and social distancing on the spread of COVID-19 in Saudi Arabia, PLOS ONE, 17 (2022), 1–40. https://doi.org/10.1371/journal.pone.0265779 doi: 10.1371/journal.pone.0265779
[38]	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. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
[39]	L. Perko, Differential Equations and Dynamical Systems, Springer, 2001. https://doi.org/10.1007/978-1-4613-0003-8.
[40]	B. E. Meserve, Fundamental Concepts of Algebra, Dover Publications, 1982.
[41]	R. K. Nagle, E. B. Saff, A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, Pearson/Addison Wesley, 2004.
[42]	M. Bensoubaya, A. Ferfera, A. Iggidr, Stabilization of nonlinear systems by use of semidefinite Lyapunov functions, Appl. Math. Lett., 12 (1999), 11–17. https://doi.org/10.1016/S0893-9659(99)00095-6 doi: 10.1016/S0893-9659(99)00095-6
[43]	J. K. Hale, H. Koçak, Dynamics and Bifurcations, Springer, 1991. https://doi.org/10.1007/978-1-4612-4426-4.
[44]	General Authority for Statistics Kingdom of Saudi Arabia, 2019. Available from: https://www.stats.gov.sa/en/1007-0.
[45]	COVID 19 Dashboard: Saudi Arabia, 2020. Available from: https://covid19.moh.gov.sa/.
[46]	H. Youssef, N. Alghamdi, M. A. Ezzat, A. A. El-Bary, A. M. Shawky, Study on the SEIQR model and applying the epidemiological rates of COVID-19 epidemic spread in Saudi Arabia, Infect. Dis. Model., 6 (2021), 678–692. https://doi.org/10.1016/j.idm.2021.04.005 doi: 10.1016/j.idm.2021.04.005
[47]	M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, 2015. https://doi.org/10.1007/978-1-4899-7612-3

This article has been cited by:

1.	Leonid Shaikhet, About one method of stability investigation for nonlinear stochastic delay differential equations, 2021, 1049-8923, 10.1002/rnc.5440
2.	Leonid Shaikhet, Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population, 2014, 11, 1551-0018, 1167, 10.3934/mbe.2014.11.1167
3.	Federico Lessio, Alberto Alma, Models Applied to Grapevine Pests: A Review, 2021, 12, 2075-4450, 169, 10.3390/insects12020169
4.	Sofia G. Seabra, Ana S.B. Rodrigues, Sara E. Silva, Ana Carina Neto, Francisco Pina-Martins, Eduardo Marabuto, Vinton Thompson, Michael R. Wilson, Selçuk Yurtsever, Antti Halkka, Maria Teresa Rebelo, Paulo A.V. Borges, José A. Quartau, Chris D. Jiggins, Octávio S. Paulo, Population structure, adaptation and divergence of the meadow spittlebug, Philaenus spumarius (Hemiptera, Aphrophoridae), revealed by genomic and morphological data, 2021, 9, 2167-8359, e11425, 10.7717/peerj.11425
5.	Leonid Shaikhet, Some Generalization of the Method of Stability Investigation for Nonlinear Stochastic Delay Differential Equations, 2022, 14, 2073-8994, 1734, 10.3390/sym14081734
6.	Leonid Shaikhet, About stability of a mathematical model of Glassy-winged Sharpshooter population under Poisson’s jumps, 2025, 08939659, 109523, 10.1016/j.aml.2025.109523

Reader Comments

Your name:*

Email:*
© 2022 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)