Through mutation, viruses constantly change, bringing into existence new variants; SARS-CoV-2 is no different. In December 2020, variants with different characteristics that could affect transmissibility and death emerged around the world of which Ghana is not an exception. To address this new phenomenon, a two-strain mathematical model of SARS-CoV-2 was formulatedto analyzed thetransmission dynamicsin Ghana. Thedisease-free equilibriumwas calculated. The basicreproduction number, R0= max{R0A, R0B} = max(0.9957945674, 1.109170840), associated with the model is computed using the next generation matrix operator. The disease-free equilibrium is found to be locally asymptotically stable when both R0A, R0B < 1, but unstable otherwise. In addition to the disease-free, the boundary equilibrium for strain A and strain B was also calculated. Using the Gershgorin’s circle theorem, it was shown that the boundary equilibrium is locally asymptotically stable when both R0A, R0B > 1, but unstable when otherwise. Simulations of the model were carried out. Results indicate that the government should intensify its efforts to vaccinate a larger proportion of the population and also recommends implementing comprehensive control measures, such as the use of face masks, social distancing, and contact tracing, to mitigate the spread of the disease.
| Published in | American Journal of Applied Mathematics (Volume 12, Issue 5) |
| DOI | 10.11648/j.ajam.20241205.15 |
| Page(s) | 149-166 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
COVID-19, SARS-CoV-2, SVEIR Transmission Dynamics, Diseases-free Equilibrium, Boundary Equilibrium, Stability Analysis, Simulation
| [1] | Danso-Addo, E., Boadi, S., Cobbinah, J. A Mathematical Model of the Transmission of COVID-19 in Ghana. American Journal of Applied Mathematics. 2023, 11(6), 119-129. |
| [2] | Jebril, N.WorldHealthOrganizationdeclaredapandemic public health menace: a systematic review of the coronavirus disease 2019 COVID-19. 2020, Vol. 1, No. 2, pp. 1-5. |
| [3] |
World Health Organisation. “World Health Organisation (WHO) Coronavirus (COVID-19) Dashboard”. Available from:
https://covid19.who.int/ [Accessed: August 1, 2021]. |
| [4] |
World Health Organisation. “World Health Organisation (WHO) Coronavirus (COVID- 19) Dashboard-Ghana”. Available from:
https://covid19.who.int/region/afro/country/gh [Accessed: August 1, 2021] |
| [5] | Halim, M. A Report on COVID-19 Variants, COVID-19 Vaccines and the Impact of the Variants on the Efficacy of the Vaccines. J Clin Med Res. 2021, Vol. 3, No. 2, pp. 1-19. |
| [6] | Duong, D.Alpha, Beta, Delta, Gamma: What’sImportant to Know About SARS-CoV-2 Variants of Concern. 2021, pp. 2-8. |
| [7] | Torjesen, I. Covid-19: Delta Variant is Now UK’s Most Dominant Strain and Spreading Through Schools. 2021, 23 pp. |
| [8] | Agoti, C. N., Ochola-Oyier, L. I., Mohammed, K. S., Lambisia, A. W., de Laurent, Z. R., Morobe, J. M., Mburu, M. W., Omuoyo, D. O., Ongera, E. M., Ndwiga, L. Genomic Surveillance Reveals the Spread Patterns of SARS-CoV-2 in Coastal Kenya During the First Two Waves. medRxiv. 2021, 12 pp. |
| [9] | Khyar, O. and Allali, K. Global Dynamics of a Multi- Strain SEIR Epidemic Model with General Incidence Rates: Application to COVID-19 Pandemic, Nonlinear Dynamics. 2020, Vol. 102, No. 1, pp. 489-509. |
| [10] | Fudolig, M. and Howard, R. The Local Stability of a Modified Multi-Strain SIR Model for Emerging Viral Strains. PloS one. 2020, Vol. 15, No. 12, pp. e24-e34. |
| [11] | Arruda, E. F., Pastore, D. H., Dias, C. M., and Das, S. S. Modeling and Optimal Control of Multi Strain Epidemics, with Application to COVID-19. 2021, pp. 2- 6. |
| [12] | Zill, D. G. A First Course in Differential Equations with Modeling Applications. Cengage Learning. 2012, 34 pp |
| [13] | Tolles, J. and Luong, T. Modeling Epidemics with Compartmental Models. Jama. 2020, Vol. 323, No. 24, pp. 2515-2516. |
| [14] | Sutton, K. M. Discretizing the SI Epidemic Model. Rose- Hulman Undergraduate Mathematics Journal. 2014, Vol. 15, No. 1, 12 pp. |
| [15] | Delamater, P. L., Street, E. J., Leslie, T. F., Yang, Y. T., and Jacobsen, K. H. Complexity of the Basic Reproduction Number. Emerging infectious diseases. 2019, Vol. 25, No. 1, pp. 1-3. |
| [16] | Anastassopoulou, C., Russo, L., Tsakris, A., and one, S. Data-Based Analysis, Modeling and Forecasting of the COVID-19 Outbreak. 2020, Vol. 15, No. 3, pp. e02 -e04. |
| [17] | Ma, Z. Dynamical Modeling and Analysis of Epidemics World Scientific. 2009, pp. 2-23. |
| [18] | Diekmann, O.; Heesterbeek, J. A. P.; Metz, J. A. J. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology. (1990-8-4), 365-382. |
| [19] | Wu, S., Tian, C., Liu, P., Guo, D., Zheng, W., Huang, X., Zhang, Y., and Liu, L. Effects of SARS-CoV-2 Mutations on Protein Structures and Intraviral Protein? Protein Interactions. Journal of medical virology. 2021, Vol. 93, No. 4, pp. 2132-2140. |
| [20] | Zhang, Z., Zeb, A., Alzahrani, E., and Iqbal, S. Crowding effects on the dynamics of COVID-19 mathematical model. Advances in Difference Equations. 2020, No. 1, pp. 1-13. |
APA Style
Cobbinah, J., Boadi, S., Crankson, M. V. (2024). Modeling the Two-Strain Dynamics of COVID-19 in Ghana Using a Logistic Growth Model. American Journal of Applied Mathematics, 12(5), 149-166. https://doi.org/10.11648/j.ajam.20241205.15
ACS Style
Cobbinah, J.; Boadi, S.; Crankson, M. V. Modeling the Two-Strain Dynamics of COVID-19 in Ghana Using a Logistic Growth Model. Am. J. Appl. Math. 2024, 12(5), 149-166. doi: 10.11648/j.ajam.20241205.15
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Download@article{10.11648/j.ajam.20241205.15,
author = {John Cobbinah and Samuella Boadi and Monica Veronica Crankson},
title = {Modeling the Two-Strain Dynamics of COVID-19 in Ghana Using a Logistic Growth Model},
journal = {American Journal of Applied Mathematics},
volume = {12},
number = {5},
pages = {149-166},
doi = {10.11648/j.ajam.20241205.15},
url = {https://doi.org/10.11648/j.ajam.20241205.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20241205.15},
abstract = {Through mutation, viruses constantly change, bringing into existence new variants; SARS-CoV-2 is no different. In December 2020, variants with different characteristics that could affect transmissibility and death emerged around the world of which Ghana is not an exception. To address this new phenomenon, a two-strain mathematical model of SARS-CoV-2 was formulatedto analyzed thetransmission dynamicsin Ghana. Thedisease-free equilibriumwas calculated. The basicreproduction number, R0= max{R0A, R0B} = max(0.9957945674, 1.109170840), associated with the model is computed using the next generation matrix operator. The disease-free equilibrium is found to be locally asymptotically stable when both R0A, R0B A and strain B was also calculated. Using the Gershgorin’s circle theorem, it was shown that the boundary equilibrium is locally asymptotically stable when both R0A, R0B > 1, but unstable when otherwise. Simulations of the model were carried out. Results indicate that the government should intensify its efforts to vaccinate a larger proportion of the population and also recommends implementing comprehensive control measures, such as the use of face masks, social distancing, and contact tracing, to mitigate the spread of the disease.},
year = {2024}
}
TY - JOUR
T1 - Modeling the Two-Strain Dynamics of COVID-19 in Ghana Using a Logistic Growth Model
AU - John Cobbinah
AU - Samuella Boadi
AU - Monica Veronica Crankson
Y1 - 2024/09/29
PY - 2024
N1 - https://doi.org/10.11648/j.ajam.20241205.15
DO - 10.11648/j.ajam.20241205.15
T2 - American Journal of Applied Mathematics
JF - American Journal of Applied Mathematics
JO - American Journal of Applied Mathematics
SP - 149
EP - 166
PB - Science Publishing Group
SN - 2330-006X
UR - https://doi.org/10.11648/j.ajam.20241205.15
AB - Through mutation, viruses constantly change, bringing into existence new variants; SARS-CoV-2 is no different. In December 2020, variants with different characteristics that could affect transmissibility and death emerged around the world of which Ghana is not an exception. To address this new phenomenon, a two-strain mathematical model of SARS-CoV-2 was formulatedto analyzed thetransmission dynamicsin Ghana. Thedisease-free equilibriumwas calculated. The basicreproduction number, R0= max{R0A, R0B} = max(0.9957945674, 1.109170840), associated with the model is computed using the next generation matrix operator. The disease-free equilibrium is found to be locally asymptotically stable when both R0A, R0B A and strain B was also calculated. Using the Gershgorin’s circle theorem, it was shown that the boundary equilibrium is locally asymptotically stable when both R0A, R0B > 1, but unstable when otherwise. Simulations of the model were carried out. Results indicate that the government should intensify its efforts to vaccinate a larger proportion of the population and also recommends implementing comprehensive control measures, such as the use of face masks, social distancing, and contact tracing, to mitigate the spread of the disease.
VL - 12
IS - 5
ER -
Department of Mathematical Science, University of Mines and Technology, Tarkwa, Ghana; Department of Mathematical Sciences, Ball State University, Muncie, USA
Department of Mathematical Science, University of Mines and Technology, Tarkwa, Ghana; Department of Mathematical Sciences, Ball State University, Muncie, USA
Department of Mathematical Science, University of Mines and Technology, Tarkwa, Ghana
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