Modelling the Dynamics of COVID-19 Disease with Contact Tracing and Isolation in Ghana
Mathematical Modelling and Applications
Volume 5, Issue 3, September 2020, Pages: 146-155
Received: Jun. 9, 2020;
Accepted: Jun. 23, 2020;
Published: Jul. 6, 2020
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Eric Neebo Wiah, Department of Mathematical Sciences, Faculty of Engineering, University of Mines and Technology, Tarkwa, Ghana
Ernest Danso-Addo, Department of Mathematical Sciences, Faculty of Engineering, University of Mines and Technology, Tarkwa, Ghana
Daniel Ekow Bentil, Department of Mathematics and Statistics and Molecular Physiology and Biophysics, University of Vermont, Burlington, USA
We have formulated a mathematical model to investigate the transmission dynamics of the current novel COVID-19 disease outbreak in Ghana. The coronavirus originated from Wuhan,, China. Majority of people who contact the disease experience mild to moderate respiratory illness and recover. The elderly and people with underlying health issues experience severe complications. A plethora of measures have been taken by the government of Ghana to curtail the disease. The model considers, among other things, quarantining and testing of immigrants, contact tracing and isolation in the form of quarantining or hospitalization, as control measures in mitigating the spread of the pandemic. Our model considers the following classes: susceptible, exposed, infectious, quarantine, treatment and recovery class. The steady-state solution was calculated and the basic reproduction number for this model calculated and used as a threshold to determine the asymptotic behaviour of the model. Our analytical and numerical results show a close dependence of the basic reproductive number on epidemic parameters. The aim of this paper was to incorporate the various intervention strategies into the model and ascertain their impact on COVID-19. Some of the methods employed in the analysis include the Next Generation Matrix and the Jacobian Matrix. Our simulations results correlate well with data and indicate that early quarantine and a high quarantine rate are crucial to the control of COVID-19. Thus, current preventative measures, such as isolation, contact tracing and treatment are, indeed, critical components in the control of COVID-19 until appropriate cure or vaccine is found.
Eric Neebo Wiah,
Daniel Ekow Bentil,
Modelling the Dynamics of COVID-19 Disease with Contact Tracing and Isolation in Ghana, Mathematical Modelling and Applications.
Vol. 5, No. 3,
2020, pp. 146-155.
J. Bryner, 1st known case of coronavirus traced back to November in China, https://www.livescience.com/first-case-coronavirus-found.html, Accessed April 18, 2020.
Centers for Disease Control and Prevention, Symptoms of Coronavirus. https://www.cdc.gov/coronavirus/2019-ncov/symptoms-testing/symptoms.html. Accessed April 18, 2020.
Ministry of Health, Ghana, COVID-19 Ghana’s outbreak response management update. https://ghanahealthservice.org/covid19/#.
G. Chowell, P. W. Fenimore, M. A. Castillo-Garsow, C. Castillo-Chavez, SARS out-breaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism. J Theor Biol. 2003; 224: 1-8.
J. M. Drazen, R. Kanapathipillai, E. W. Campion, E. J. Rubin, S. M. Hammer and S. Morrissey, Ebola and quarantine. New England Journal of Medicine, 371, (2014), 2029-2030.
M. A. Safi and A. B. Gumel, Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine, Computers and Mathematics with Applications, 61 (2011) 3044–3070.
N. T. J. Bailey, The Mathematical Theory of Infectious Diseases, Second Edition, Hafner, New York, (1975).
J. T. Wu, K. Leung, and 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.
S. Pengpeng, C. Shengli and F. Peihua, SEIR Transmission dynamics model of 2019 nCoV coronavirus with considering the weak infectious ability and changes in latency duration. medRxiv preprint doi: https://doi.org/10.1101/2020.02.16.20023655.
C. Yang and J. Wang, A mathematical model for the novel coronavirus epidemic in Wuhan, China. Mathematical Biosciences and Engineering Volume 17, Issue 3, 2708–2724.
X. Chang, M. Liu, Z. Jin and J. Wang, Studying on the impact of media coverage on the spread of COVID-19 in Hubei Province, China. Mathematical Biosciences and Engineering Volume 17, (2020) Issue 4, 3147–3159.
V. Capasso, Mathematical structures of epidemic systems, In Lecture Notes in Biomathematics, Volume 97, (1993), Springer-Verlag, Berlin.
C. Huang, Y. Wang, X. Li, L. Ren, J. Zhao and Y. Hu, "Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China." The Lancet 395 (10223): (2020) 497-506. https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30183-5/fulltext.
X. Yang, L. Chen and J. Chen, Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models, Comput. Math. Appl., 32, (1996) 109–116.
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosc., 180, (2002), 29–48.
D. E. Bentil and J. D. Murray, Modelling Bovine Tuberculosis Infection in Badgers. Journal of Animal Ecology, 62, (1993), 239–250.
E. N. Wiah, O. D. Makinde and I. A. Adetunde, Optimal Control of Hepatitis B Virus Disease in a Population with Infected Immigrants, Eng. Math. Let, (2015): 8 ISSN: 2049-9337.