Research article Special Issues

A mathematical model for human-to-human transmission of COVID-19: a case study for Turkey's data


  • Received: 12 July 2021 Accepted: 01 September 2021 Published: 05 November 2021
  • In this study, a mathematical model for simulating the human-to-human transmission of the novel coronavirus disease (COVID-19) is presented for Turkey's data. For this purpose, the total population is classified into eight epidemiological compartments, including the super-spreaders. The local stability and sensitivity analysis in terms of the model parameters are discussed, and the basic reproduction number, $ R_{0} $, is derived. The system of nonlinear ordinary differential equations is solved by using the Galerkin finite element method in the FEniCS environment. Furthermore, to guide the interested reader in reproducing the results and/or performing their own simulations, a sample solver is provided. Numerical simulations show that the proposed model is quite convenient for Turkey's data when used with appropriate parameters.

    Citation: Süleyman Cengizci, Aslıhan Dursun Cengizci, Ömür Uğur. A mathematical model for human-to-human transmission of COVID-19: a case study for Turkey's data[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 9787-9805. doi: 10.3934/mbe.2021480

    Related Papers:

  • In this study, a mathematical model for simulating the human-to-human transmission of the novel coronavirus disease (COVID-19) is presented for Turkey's data. For this purpose, the total population is classified into eight epidemiological compartments, including the super-spreaders. The local stability and sensitivity analysis in terms of the model parameters are discussed, and the basic reproduction number, $ R_{0} $, is derived. The system of nonlinear ordinary differential equations is solved by using the Galerkin finite element method in the FEniCS environment. Furthermore, to guide the interested reader in reproducing the results and/or performing their own simulations, a sample solver is provided. Numerical simulations show that the proposed model is quite convenient for Turkey's data when used with appropriate parameters.



    加载中


    [1] I. Holmdahl, C. Buckee, Wrong but useful–what Covid-19 epidemiologic models can and cannot tell us, New Engl. J. Med., 383 (2020), 303–305. doi: 10.1056/NEJMp2016822
    [2] W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond., 115 (1927), 700–721.
    [3] F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2012.
    [4] H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599–653. doi: 10.1137/S0036144500371907
    [5] J. D. Murray, Mathematical Biology: I. An Introduction, 3rd edition, Springer-Verlag, New York, 2002.
    [6] J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, 3rd edition, Springer-Verlag, New York, 2003.
    [7] E. E. Holmes, M. A. Lewis, J. E. Banks, R. R. Veit, Partial differential equations in ecology: Spatial interactions and population dynamics, Ecology, 75 (1994), 17–29. doi: 10.2307/1939378
    [8] O. Diekmann, H. Heesterbeek, T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Princeton University Press, 2013.
    [9] J. Müller, C. Kuttler, Methods and Models in Mathematical Biology: Deterministic and Stochastic Approaches, Springer-Verlag, Berlin Heidelberg, 2015.
    [10] G. Bocharov, V. Volpert, B. Ludewig, A. Meyerhans, Mathematical Immunology of Virus Infections, Springer International Publishing, 2018.
    [11] M. Y. Li, An Introduction to Mathematical Modeling of Infectious Diseases, Princeton University Press, 2018.
    [12] M. Martcheva, An Introduction to Mathematical Epidemiology, Springer US, 2015.
    [13] K. P. Hadeler, Topics in Mathematical Biology, Springer International Publishing, 2017.
    [14] S. Ahmad, A. Ullah, Q. M. Al-Mdallal, H. Khan, K. Shah, A. Khan, Fractional order mathematical modeling of COVID-19 transmission, Chaos Solitons Fractal., 139 (2020), 110256. doi: 10.1016/j.chaos.2020.110256
    [15] H. S. Badr, H. Du, M. Marshall, E. Dong, M. M. Squire, L. M. Gardner, Association between mobility patterns and COVID-19 transmission in the USA: a mathematical modelling study, The Lancet Infect. Dis., 20 (2020), 1247–1254. doi: 10.1016/S1473-3099(20)30553-3
    [16] A. L. Bertozzi, E. Franco, G. Mohler, M. B. Short, D. Sledge, The challenges of modeling and forecasting the spread of COVID-19, Proc. Natl. A. Sci., 117 (2020), 16732–16738. doi: 10.1073/pnas.2006520117
    [17] R. Cherniha, V. Davydovych, A mathematical model for the COVID-19 outbreak and its applications, Symmetry, 12 (2020), 990. doi: 10.3390/sym12060990
    [18] H. Coşkun, N. Yıldırım, S. Gündüz, The spread of COVID-19 virus through population density and wind in Turkey cities, Sci. Total Environ., 751 (2021), 141663. doi: 10.1016/j.scitotenv.2020.141663
    [19] S. Bugalia, V. P. Bajiya, J. P. Tripathi, M. T. Li, G. Q. Sun, Mathematical modeling of COVID-19 transmission: the roles of intervention strategies and lockdown, Math. Biosci. Eng., 17 (2020), 5961–5986. doi: 10.3934/mbe.2020318
    [20] B. Ivorra, M. R. Ferrández, M. Vela-Pérez, A. M. Ramos, Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China, Commun. Nonlinear Sci., 88 (2020), 105303. doi: 10.1016/j.cnsns.2020.105303
    [21] M. Medrek, Z. Pastuszak, Numerical simulation of the novel coronavirus spreading, Expert Syst. Appl., 166 (2021), 114109. doi: 10.1016/j.eswa.2020.114109
    [22] D. Okuonghae, A. Omame, Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria, Chaos Solitons Fractal., 139 (2020), 110032. doi: 10.1016/j.chaos.2020.110032
    [23] Z. Feng, J. W. Glasser, A. N. Hill, On the benefits of flattening the curve: A perspective, Math. Biosci., 326 (2020), 108389. doi: 10.1016/j.mbs.2020.108389
    [24] T. M. Chen, J. Rui, Q. P. Wang, Z. Y. Zhao, J. A. Cui, L. Yin, A mathematical model for simulating the phase-based transmissibility of a novel coronavirus, Infect. Dis. Poverty, 9 (2020).
    [25] P. Samui, J. Mondal, S. Khajanchi, A mathematical model for COVID-19 transmission dynamics with a case study of India, Chaos Solitons Fractal., 140 (2020), 110173. doi: 10.1016/j.chaos.2020.110173
    [26] N. H. Tuan, H. Mohammadi, S. Rezapour, A mathematical model for COVID-19 transmission by using the Caputo fractional derivative, Chaos Solitons Fractal., 140 (2020), 110107. doi: 10.1016/j.chaos.2020.110107
    [27] S. Çakan, Dynamic analysis of a mathematical model with health care capacity for COVID-19 pandemic, Chaos Solitons Fractal., 139 (2020), 110033. doi: 10.1016/j.chaos.2020.110033
    [28] R. P. Yadav, Renu Verma, A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China, Chaos Solitons Fractal., 140 (2020), 110124. doi: 10.1016/j.chaos.2020.110124
    [29] A. Atangana, Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?, Chaos Solitons Fractal., 136 (2020), 109860. doi: 10.1016/j.chaos.2020.109860
    [30] E. Atangana, A. Atangana, Facemasks simple but powerful weapons to protect against COVID-19 spread: Can they have sides effects?, Results Phys., 19 (2020), 103425. doi: 10.1016/j.rinp.2020.103425
    [31] M. A. Khan, A. Atangana, E. Alzahrani, Fatmawati, The dynamics of COVID-19 with quarantined and isolation, Adv. Differ. Equation, 2020 (2020), 1687–1847.
    [32] A. Viguerie, A. Veneziani, G. Lorenzo, D. Baroli, N. Aretz-Nellesen, A. Patton, et al., Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study, Comput. Mech., 66 (2020), 1131–1152. doi: 10.1007/s00466-020-01888-0
    [33] A. Viguerie, G. Lorenzo, F. Auricchio, D. Baroli, T. J. R. Hughes, A. Patton, et al., Simulating the spread of COVID-19 via a spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion, Appl. Math. Lett., 111 (2021), 106617. doi: 10.1016/j.aml.2020.106617
    [34] H. Zhao, Z. Feng, Staggered release policies for COVID-19 control: Costs and benefits of relaxing restrictions by age and risk, Math. Biosci., 326 (2020), 108405. doi: 10.1016/j.mbs.2020.108405
    [35] Y. N. Kyrychko, K. B. Blyuss, I. Brovchenko, Mathematical modelling of the dynamics and containment of COVID-19 in Ukraine, Sci. Rep., 10 (2020), 19662. doi: 10.1038/s41598-020-76710-1
    [36] K. Sarkar, S. Khajanchi, J. J. Nieto, Modeling and forecasting the COVID-19 pandemic in India, Chaos Solitons Fractal., 139 (2020), 110049. doi: 10.1016/j.chaos.2020.110049
    [37] A. S. Shaikh, I. N. Shaikh, K. S. Nisar, A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control, Adv. Differ. Equation, 2020 (2020), 373. doi: 10.1186/s13662-020-02834-3
    [38] K. Naeem, M. Riaz, X. Peng, D. Afzal, Pythagorean $m$-polar fuzzy topology with TOPSIS approach in exploring most effectual method for curing from COVID-19, Inter. J. Biomath., 13 (2020), 2050075. doi: 10.1142/S1793524520500758
    [39] S. Saha, G. P. Samanta, J. J. Nieto, Epidemic model of COVID-19 outbreak by inducing behavioural response in population, Nonlinear Dynam., 102 (2020), 455–487. doi: 10.1007/s11071-020-05896-w
    [40] N. Moradian, H. D. Ochs, C. Sedikies, M. R. Hamblin, C. A. Camargo, J. A. Martinez, et al., The urgent need for integrated science to fight COVID-19 pandemic and beyond, J. Transl. Med., 18 (2020), 205. doi: 10.1186/s12967-020-02364-2
    [41] K. Mohamed, N. Rezaei, COVID-19 pandemic is not the time of trial and error, Am. J. Emerg. Med., 46 (2021), 774–775. doi: 10.1016/j.ajem.2020.09.020
    [42] S. A. Cheema, T. Kifayat, A. R. Rahman, U. Khan, A. Zaib, I. Khan, et al., Is social distancing, and quarantine effective in restricting COVID-19 outbreak? Statistical evidences from Wuhan, China, Comput. Mater. Con., 66 (2021), 1977–1985.
    [43] E. Kuhl, Data-driven modeling of COVID-19–Lessons learned, Extreme Mech. Lett., 40 (2020), 100921. doi: 10.1016/j.eml.2020.100921
    [44] M. M. Sakr, N. S. Elsayed, G. S. El-Housseiny, Latest updates on SARS-CoV-2 genomic characterization, drug, and vaccine development: a comprehensive bioinformatics review, Microb. Pathogenesis, 154 (2021), 104809. doi: 10.1016/j.micpath.2021.104809
    [45] S. Moore, E. M. Hill, M. J. Tildesley, L. Dyson. M. J. Keeling, Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study, Lancet Infect. Dis., 21 (2021), 793–802. doi: 10.1016/S1473-3099(21)00143-2
    [46] L. Forchette, W. Sebastian, T. Liu, A comprehensive review of COVID-19 virology, vaccines, variants, and therapeutics, Curr. Med. Sci., 9 (2021), 1–15.
    [47] F. Ndaïrou, D. F. M. Torres, Mathematical analysis of a fractional COVID-19 model applied to Wuhan, Spain and Portugal, Axioms, 10 (2021), 135. doi: 10.3390/axioms10030135
    [48] I. A. Baba, A. Yusuf, K. S. Nisar, A. H. Abdel-Aty, T. A. Nofal, Mathematical model to assess the imposition of lockdown during COVID-19 pandemic, Results Phys., 20 (2021), 103716. doi: 10.1016/j.rinp.2020.103716
    [49] J. Danane, K. Allali, Z. Hammouch, K. S. Nisar, Mathematical analysis and simulation of a stochastic COVID-19 Lévy jump model with isolation strategy, Results Phys., 23 (2021), 103994. doi: 10.1016/j.rinp.2021.103994
    [50] T. Khan, G. Zaman, Y. El-Khatib. Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model, Alex. Eng. J., 24 (2021), 104004.
    [51] S. Khajanchi, K. Sarkar, J. Mondal, K. S. Nisar, S. F. Abdelwahab, Mathematical modeling of the COVID-19 pandemic with intervention strategies, Results Phys., 25 (2021), 104285. doi: 10.1016/j.rinp.2021.104285
    [52] H. Singh, H. M. Srivastava, Z. Hammouch, K. S. Nisar, Numerical simulation and stability analysis for the fractional-order dynamics of COVID-19, Results Phys., 20 (2021), 103722. doi: 10.1016/j.rinp.2020.103722
    [53] F. Ndaïrou, I. Area, J. J. Nieto, D. F. M. Torres, Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan, Chaos Solitons Fractal., 135 (2020), 109846. doi: 10.1016/j.chaos.2020.109846
    [54] F. Ndaïrou, I. Area, G. Bader, J. J. Nieto, D. F. M. Torres, Corrigendum to "mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan", Chaos Solitons Fractal., 141 (2020), 110311. doi: 10.1016/j.chaos.2020.110311
    [55] 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
    [56] P. van den Driessche, Reproduction numbers of infectious disease models, Infect. Dis. Model., 2 (2017), 288–303.
    [57] M. G. Larson, F. Bengzon, The Finite Element Method: Theory, Implementation, and Applications, Springer-Verlag, Berlin Heidelberg, 2013.
    [58] M. S. Gockenbach, Understanding and Implementing the Finite Element Method, vol. 97, SIAM, Philadelphia, 2006.
    [59] S. Brenner, R. Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 2007.
    [60] A. Logg, K. A. Mardal, G. Wells, Automated solution of differential equations by the finite element method: The FEniCS book, Springer Science Business Media, 2012.
    [61] B. E. Abali, Computational Reality: Solving Nonlinear and Coupled Problems in Continuum Mechanics, Springer, 2016.
    [62] H. P. Langtangen, K. A. Mardal, Introduction to Numerical Methods for Variational Problems, Springer International Publishing, 2019.
    [63] Worldometers, COVID-19 Coronavirus Pandemic, (2020). Available from: https://www.worldometers.info/coronavirus/country/turkey/.
    [64] N. Chitnis, J. M. Hyman, J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272–1296. doi: 10.1007/s11538-008-9299-0
    [65] H. S. Rodrigues, M. T. T. Monteiro, D. F. M. Torres, Sensitivity analysis in a dengue epidemiological model, in Conference Papers in Mathematics, 2013 (2013), 1–7.
  • Reader Comments
  • © 2021 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2401) PDF downloads(177) Cited by(0)

Article outline

Figures and Tables

Figures(5)  /  Tables(2)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog