Analysis of COVID-19 outbreak in Democratic Republic of the Congo using fractional operators

Aqeel Ahmad; Cicik Alfiniyah; Ali Akgül; Aeshah A. Raezah; Aqeel Ahmad; Cicik Alfiniyah; Ali Akgül; Aeshah A. Raezah

doi:10.3934/math.20231309

AIMS Mathematics

2023, Volume 8, Issue 11: 25654-25687. doi: 10.3934/math.20231309

Previous Article Next Article

Research article Special Issues

Analysis of COVID-19 outbreak in Democratic Republic of the Congo using fractional operators

1.
Department of Mathematics, Ghazi University D G Khan 32200, Pakistan
2.
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Indonesia
3.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
4.
Art and Science Faculty, Department of Mathematics, Siirt 56100, Turkey
5.
Mathematics Research Center, Department of Mathematics, Near East Boulevard, 99138, Nicosia /Mersin 10, Turkey
6.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia

Received: 12 May 2023 Revised: 06 July 2023 Accepted: 11 July 2023 Published: 05 September 2023
MSC : 03C45, 33E12

The spread of COVID-19 in the Democratic Republic of the Congo is investigated in this work using fractional operators. To model the spread of the current COVID-19 variant among different age groups, we employ the epidemic scenario in the Democratic Republic of the Congo as a case study. In this study, the key characteristics of an epidemic problem such as COVID-19 are validated for existence and positivity, and unique solutions are demonstrated by applying certain findings from fixed-point theory. We also use the first derivative function to confirm the overall stability of the proposed system. The established methodology, which examines the impact of COVID-19 on various age groups, is highly sophisticated. Additionally, we use a method created by Atangana to solve the given model. This method stands as one of the most advanced approaches for addressing infectious problems; we also conduct an error analysis to identify and rectify any inaccuracies. Lastly, we assess the parameters to determine the effects of illness, and we provide numerical simulations implemented in MATLAB. These simulations illustrate the behavior of this infectious disease among various age groups in the Democratic Republic of the Congo.
- boundedness,
- global stability,
- uniqueness,
- positivity,
- Mittag-Leffler
Citation: Aqeel Ahmad, Cicik Alfiniyah, Ali Akgül, Aeshah A. Raezah. Analysis of COVID-19 outbreak in Democratic Republic of the Congo using fractional operators[J]. AIMS Mathematics, 2023, 8(11): 25654-25687. doi: 10.3934/math.20231309

Related Papers:

Abstract

The spread of COVID-19 in the Democratic Republic of the Congo is investigated in this work using fractional operators. To model the spread of the current COVID-19 variant among different age groups, we employ the epidemic scenario in the Democratic Republic of the Congo as a case study. In this study, the key characteristics of an epidemic problem such as COVID-19 are validated for existence and positivity, and unique solutions are demonstrated by applying certain findings from fixed-point theory. We also use the first derivative function to confirm the overall stability of the proposed system. The established methodology, which examines the impact of COVID-19 on various age groups, is highly sophisticated. Additionally, we use a method created by Atangana to solve the given model. This method stands as one of the most advanced approaches for addressing infectious problems; we also conduct an error analysis to identify and rectify any inaccuracies. Lastly, we assess the parameters to determine the effects of illness, and we provide numerical simulations implemented in MATLAB. These simulations illustrate the behavior of this infectious disease among various age groups in the Democratic Republic of the Congo.

References

[1]	T. F. Booth, B. Kournikakis, N. Bastien, J. Ho, D. Kobasa, L. Stadnyk, et al., Detection of airborne severe acute respiratory syndrome (SARS) coronavirus and environmental contamination in SARS outbreak units, J. Infect. Dis., 191 (2005), 1472–1477. https://doi.org/10.1086/429634 doi: 10.1086/429634
[2]	P. Bahl, C. Doolan, C. de Silva, A. A. Chughtai, L. Bourouiba, C. R. MacIntyre, Airborne or droplet precautions for health workers treating coronavirus disease 2019? J. Infect. Dis., 225 (2022), 1561–1568. https://doi.org/10.1093/infdis/jiaa189
[3]	F. Zhou, T. Yu, R. Du, G. Fan, Y. Liu, Z. Liu, et al., Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: A retrospective cohort study, Lancet, 395 (2022), 1054–1062. https://doi.org/10.1016/S0140-6736(20)30566-3 doi: 10.1016/S0140-6736(20)30566-3
[4]	F. Gambaro, S. Behillil, A. Baidaliuk, F. Donati, M. Albert, A. Alexandru, et al., Introductions and early spread of SARSCoV-2 in France, 24 January to 23 March 2020, Euro Surveill., 25 (2020), 2001200. https://doi.org/10.2807/1560-7917.ES.2020.25.26.2001200 doi: 10.2807/1560-7917.ES.2020.25.26.2001200
[5]	H. Li, S. Wang, F. Zhong, W. Bao, Y. Li, L. Liu, et al., Age-dependent risks of incidence and mortality of COVID-19 in hubei province and other parts of China, Front. Med., 7 (2020), 190. https://doi.org/10.3389/fmed.2020.00190 doi: 10.3389/fmed.2020.00190
[6]	T. Chen, D. Wu, H. Chen, W. Yan, D. Yang, G. Chen, et al., Clinical characteristics of 113 deceased patients with coronavirus disease 2019: Retrospective study, BMJ, 368 (2019), m1091. https://doi.org/10.1136/bmj.m1091 doi: 10.1136/bmj.m1091
[7]	S. Cui, S. Chen, X. Li, S. Liu, F. Wang, Prevalence of venous thromboembolism in patients with severe novel coronavirus pneumonia, J. Thromb. Haemost., 18 (2020), 1421–1424. https://doi.org/10.1111/jth.14830 doi: 10.1111/jth.14830
[8]	L. Ferretti, C. Wymant, M. Kendall, L. Zhao, A. Nurtay, L. Abeler-Dorner, et al., Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing, Science, 368 (2020), 6491. https://doi.org/10.1126/science.abb6936 doi: 10.1126/science.abb6936
[9]	Y. Liu, L. M. Yan, L. Wan, T. X. Xiang, A. Le, J. M. Liu, et al., Viral dynamics in mild and severe cases of COVID-19, Lancet Infect. Dis., 20 (2020), 656–657. https://doi.org/10.1016/S1473-3099(20)30232-2 doi: 10.1016/S1473-3099(20)30232-2
[10]	D. He, S. Zhao, Q. Lin, Z. Zhuang, P. Cao, M. H. Wang, et al., The relative transmissibility of asymptomatic COVID-19 infections among close contacts, Int. J. Infect. Dis., 94 (2020), 145–147. https://doi.org/10.1016/j.ijid.2020.04.034 doi: 10.1016/j.ijid.2020.04.034
[11]	World Health Organization, Coronavirus disease 2019 (COVID-19): Situation report, 2020.
[12]	S. Kasereka, N. Kasoro, A. P. Chokki, A hybrid model for modeling the spread of epidemics: Theory and simulation, In: 2014 4th International Symposium ISKO-Maghreb: Concepts and Tools for knowledge Management (ISKO-Maghreb), Algiers, Algeria, 2014, 1–7. https://doi.org/10.1109/ISKO-Maghreb.2014.7033457
[13]	S. Kasereka, Y. Le Strat, L. Leon, Estimation of infection force of hepatitis c virus among drug users in France, In: Recent advances in nonlinear dynamics and synchronization. Studies in systems, decision and control, Springer, Cham, 109 (2018), 319–344. https://doi.org/10.1007/978-3-319-58996-1_15
[14]	A. M. Ndondo, J. M. W. Munganga, J. N. M. Mwambakana, C. M. Saad-Roy, P. Van den Driessche, R. Walo, Analysis of a model of gambiense sleeping sickness in humans and cattle, J. Biol. Dyn., 10 (2016), 347–365. https://doi.org/10.1080/17513758.2016.1190873 doi: 10.1080/17513758.2016.1190873
[15]	E. F. D. Goufof, R. Maritz, J. Munganga, Some properties of the Kermack-McKendrick epidemic model with fractional derivative and nonlinear incidence, Adv. Differ. Equ., 2014 (2014), 278. https://doi.org/10.1186/1687-1847-2014-278 doi: 10.1186/1687-1847-2014-278
[16]	N. M. Apollinaire, W. O. Rebecca, M. Y. Vala-ki-sisa, Optimal control of a model of gambiense sleeping sickness in humans and cattle, Amer. J. Appl. Math., 4 (2016), 204–216. https://doi.org/10.11648/j.ajam.20160405.12 doi: 10.11648/j.ajam.20160405.12
[17]	S. K. Kabunga, E. F. D. Goufo, V. H. Tuong, Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo, Adv. Differ. Equ., 2020 (2020), 642. https://doi.org/10.1186/s13662-020-03091-0 doi: 10.1186/s13662-020-03091-0
[18]	S. K. Kabunga, E. F. D. Goufo, V. H. Tuong, K. Kyamakya, A stochastic agent-based model and simulation for controlling the spread of tuberculosis in a mixed population structure, In: Developments of artificial intelligence technologies in computation and robotics, 14th International FLINS Conference (FLINS 2020), Cologne, Germany, 2020,659–666. https://doi.org/10.1142/9789811223334_0079
[19]	S. S. Nadim, I. Ghosh, J. Chattopadhyay, Short-term predictions and preventionstrategies for covid-2019: A model based study, Appl. Math. Comput., 404 (2021), 126251. https://doi.org/10.1016/j.amc.2021.126251 doi: 10.1016/j.amc.2021.126251
[20]	M. A. Khan, A. Atangana, Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative, Alex. Eng. J., 59 (2020), 2379–2389. https://doi.org/10.1016/j.aej.2020.02.033 doi: 10.1016/j.aej.2020.02.033
[21]	R. Resmawan, L. Yahya, Sensitivity analysis of mathematical model of coronavirus disease (COVID-19) transmission, CAUCHY-Jurnal Matematika Murni dan Aplikasi, 6 (2020), 91–99.
[22]	K. Shah, T. Abdeljawad, I. Mahariq, F. Jarad, 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 doi: 10.1155/2020/5098598
[23]	S. T. M. Thabet, M. S. Abdo, K. Shah, T. Abdeljawad, Study of transmission dynamics of COVID-19 mathematical model under abc fractional order derivative, Results Phys., 19 (2020), 103507. https://doi.org/10.1016/j.rinp.2020.103507 doi: 10.1016/j.rinp.2020.103507
[24]	S. S. Redhwan, M. S. Abdo, K. Shah, T. Abdeljawad, S. Dawood, H. A. Abdo, et al., Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator, Results Phys., 19 (2020), 103610. https://doi.org/10.1016/j.rinp.2020.103610 doi: 10.1016/j.rinp.2020.103610
[25]	R. U. Din, K. Shah, I. Ahmad, T. Abdeljawad, 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 doi: 10.1186/s13662-020-02783-x
[26]	Z. Zhang, A. Zeb, S. Hussain, E. Alzahrani, Dynamics of COVID-19 mathematical model with stochastic perturbation, Adv Differ. Equ., 2020 (2020), 451. https://doi.org/10.1186/s13662-020-02909-1 doi: 10.1186/s13662-020-02909-1
[27]	R. Ud Din, A. R. Seadawy, K. Shah, A. Ullah, D. Baleanu, Study of global dynamics of COVID-19 via a new mathematical model, Results Phys., 19 (2020), 103468. https://doi.org/10.1016/j.rinp.2020.103468 doi: 10.1016/j.rinp.2020.103468
[28]	M. Caputo, M. Fabrizio, A new definition of fractional derivatives without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 73–85. https://doi.org/10.12785/pfda/010201 doi: 10.12785/pfda/010201
[29]	A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel theory and application to heat transfer model, 2016, arXiv: 1602.03408.

Reader Comments

Your name:*

Email:*
© 2023 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)