The year 2020 brought about a pandemic that caught most of the world population by surprise and wreaked unimaginable havoc before any form of effective reaction could be put in place. COVID-19 is proving to be an epidemic that keeps on having an upsurge whenever it looks like it is being curbed. This pandemic has led to continuous strategizing on approaches to quelling the surge. The recent and welcome introduction of vaccines has led to renewed optimism for the population at large. The introduction of vaccines has led to the need to investigate the effect of vaccination among other control measures in the fight against COVID-19. In this study, we develop a mathematical model that captures the dynamics of the disease taking into consideration some measures that are easier to implement majorly within the African context. We consider quarantine and vaccination as control measures and investigate the efficacy of these measures in curbing the reproduction rate of the disease. We analyze the local stability of the disease-free equilibrium point. We also perform sensitivity analysis of the effective reproduction number to determine which parameters significantly lowers the effective reproduction number. The results obtained suggest that quarantine and a vaccine with at least $ 75\% $ efficacy and reducing transmission probability through sanitation and wearing of protective gears can significantly reduce the number of secondary infections.
Citation: Shina D. Oloniiju, Olumuyiwa Otegbeye, Absalom E. Ezugwu. Investigating the impact of vaccination and non-pharmaceutical measures in curbing COVID-19 spread: A South Africa perspective[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 1058-1077. doi: 10.3934/mbe.2022049
The year 2020 brought about a pandemic that caught most of the world population by surprise and wreaked unimaginable havoc before any form of effective reaction could be put in place. COVID-19 is proving to be an epidemic that keeps on having an upsurge whenever it looks like it is being curbed. This pandemic has led to continuous strategizing on approaches to quelling the surge. The recent and welcome introduction of vaccines has led to renewed optimism for the population at large. The introduction of vaccines has led to the need to investigate the effect of vaccination among other control measures in the fight against COVID-19. In this study, we develop a mathematical model that captures the dynamics of the disease taking into consideration some measures that are easier to implement majorly within the African context. We consider quarantine and vaccination as control measures and investigate the efficacy of these measures in curbing the reproduction rate of the disease. We analyze the local stability of the disease-free equilibrium point. We also perform sensitivity analysis of the effective reproduction number to determine which parameters significantly lowers the effective reproduction number. The results obtained suggest that quarantine and a vaccine with at least $ 75\% $ efficacy and reducing transmission probability through sanitation and wearing of protective gears can significantly reduce the number of secondary infections.
| [1] |
F. Brauer, Mathematical epidemiology: Past, present, and future, Infect. Dis. Modell., 2 (2017), 113–127. doi:10.1016/j.idm.2017.02.001. doi: 10.1016/j.idm.2017.02.001
|
| [2] |
D. S. Jones, History in a crisis—lessons for COVID-19, N. Engl. J. Med., 382 (2020), 1681–1683. doi:10.1056/NEJMp2004361. doi: 10.1056/NEJMp2004361
|
| [3] |
T. P. Velavan, C. G. Meyer, The COVID-19 epidemic, Trop. Med. Int. Health, 25 (2020), 278. doi:10.1111/tmi.13383. doi: 10.1111/tmi.13383
|
| [4] | D. Tyrrell, M. Bynoe, Cultivation of viruses from a high proportion of patients with colds, Lancet, (1966), 76–7. |
| [5] | J. Guarner, Three emerging coronaviruses in two decades: the story of SARS, MERS, and now COVID-19, (2020), 420–421. |
| [6] | A. S. Fauci, H. C. Lane, R. R. Redfield, COVID-19: Navigating the uncharted, N. Engl. J. Med., (2020), 1268–1269. |
| [7] |
T. V. Porgo, S. L. Norris, G. Salanti, L. F. Johnson, J. A. Simpson, N. Low, et al., The use of mathematical modeling studies for evidence synthesis and guideline development: A glossary, Res. Synth. Methods, 10 (2019), 125–133. doi:10.1002/jrsm.1333. doi: 10.1002/jrsm.1333
|
| [8] | A. E. Ezugwu, I. A. T. Hashem, O. N. Oyelade, M. Almutari, M. A. Al-Garadi, I. N. Abdullahi, et al, A novel smart city-based framework on perspectives for application of machine learning in combating covid-19, BioMed Res. Int., 2021 (2021), 5546790. doi: 10.1155/2021/5546790. |
| [9] | F. Brauer, C. Castillo-Chavez, Z. Feng, Mathematical models in epidemiology, Springer, 2019. |
| [10] |
S. M. Kassa, J. B. Njagarah, Y. A. Terefe, Analysis of the mitigation strategies for COVID-19: from mathematical modelling perspective, Chaos, Solitons Fractals, 138 (2020), 109968. doi:10.1016/j.chaos.2020.109968. doi: 10.1016/j.chaos.2020.109968
|
| [11] |
F. Ndairou, I. Area, J. J. Nieto, D. F. Torres, Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan, Chaos, Solitons Fractals, 135 (2020), 109846. doi:10.1016/j.chaos.2020.109846. doi: 10.1016/j.chaos.2020.109846
|
| [12] |
J. Zhang, M. Litvinova, Y. Liang, Y. Wang, W. Wang, S. Zhao, et al., Changes in contact patterns shape the dynamics of the COVID-19 outbreak in China, Science, 369 (2020), 1481–1486. doi:10.1126/science.abb8001. doi: 10.1126/science.abb8001
|
| [13] | O. Bargain, A. Ulugbek, Poverty and COVID-19 in Developing Countries, Bordeaux University, 2020. HAL Id: hal-03258229. |
| [14] |
B. C. Olopade, H. Okodua, M. Oladosun, A. J. Asaleye, Human capital and poverty reduction in OPEC member-countries, Heliyon, 5 (2019), e02279. doi:10.1016/j.heliyon.2019.e02279. doi: 10.1016/j.heliyon.2019.e02279
|
| [15] |
N. Stiegler, J. P. Bouchard, South Africa: Challenges and successes of the COVID-19 lockdown, Annales Médico-psychologiques, revue psychiatrique, 178 (2020), 695–698. doi:10.1016/j.amp.2020.05.006. doi: 10.1016/j.amp.2020.05.006
|
| [16] |
S. M. Garba, J. M.-S. Lubuma, B. Tsanou, Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa, Math. Biosci., 328 (2020), 108441. doi:10.1016/j.mbs.2020.108441. doi: 10.1016/j.mbs.2020.108441
|
| [17] |
C. Arndt, R. Davies, S. Gabriel, L. Harris, K. Makrelov, S. Robinson, et al., COVID-19 lockdowns, income distribution, and food security: An analysis for South Africa, Global Food Secur., 26 (2020), 100410. doi:10.1016/j.gfs.2020.100410. doi: 10.1016/j.gfs.2020.100410
|
| [18] | K. Megget, Even COVID-19 can't kill the anti-vaccination movement, BMJ, 369 (2020). doi: 10.1136/bmj.m2184. |
| [19] |
S. S. DeRoo, N. J. Pudalov, L. Y. Fu, Planning for a COVID-19 Vaccination Program, JAMA, 323 (2020), 2458–2459. doi:10.1001/jama.2020.8711. doi: 10.1001/jama.2020.8711
|
| [20] | Worldometers, 2020. Available from: worldometers.info/coronavirus/country/south-africa/. |
| [21] | World Bank Data, 2020. Available from: data.worldbank.org/indicator. |
| [22] |
J. Heesterbeek, K. Dietz, The concept of $R_0$ in epidemic theory, Stat. Neerl., 50 (1996), 89–110. doi:10.1111/j.1467-9574.1996.tb01482.x. doi: 10.1111/j.1467-9574.1996.tb01482.x
|
| [23] |
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. doi: 10.1016/S0025-5564(02)00108-6
|
| [24] | M. Martcheva, An introduction to mathematical epidemiology, Springer, 61 (2015). |
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Shina D. Oloniiju, Olumuyiwa Otegbeye, Absalom E. Ezugwu. Investigating the impact of vaccination and non-pharmaceutical measures in curbing COVID-19 spread: A South Africa perspective[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 1058-1077. doi: 10.3934/mbe.2022049
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