[1] World Health Organization, Coronavirus disease COVID-19 pandemic, WHO, Available at: https://www.who.int/emergencies/diseases/novel-coronavirus-2019, Accessed 15 July 2022.
[2] M. Ali, S. T. H. Shah, M. Imran and A. Khan, The role of asymptomatic class, quarantine and isolation in the transmission of COVID-19, J. Biol. Dyn. 14 (2020) 389 - 408, https://doi.org/10.1080/17513758.2020.1773000.
[3] S. P. Gatyeni, F. Chirove and F. Nyabadza, Modelling the potential impact of stigma on the transmission dynamics of COVID-19 in South Africa, Mathematics 10 (2022) #3253, https://doi.org/10.3390/math10183253.
[4] S. Khajanchi and K. Sarkar, Forecasting the daily and cumulative number of cases for the COVID-19 pandemic in India, Chaos 30 (2020) #071101, https://doi.org/10.1063/5.0016240.
[5] S. Khajanchi, K. Sarkar, J. Mondal, K. S. Nisar and S. F. Abdelwahab, Mathematical modeling of the COVID-19 pandemic
with intervention strategies, Results Phys. 25 (2021) #3104285, https://doi.org/10.1016/j.rinp.2021.104285.
[6] P. Samui, J. Mondal and S. Khajanchi, A mathematical model for COVID-19 transmission dynamics with a case study of India, Chaos Solitons Fractals 140 (2020) #110173, https://doi.org/10.1016/j.chaos.2020.110173.
[7] R. Kumar Rai, P. Kumar Tiwari and S. Khajanchi, Modeling the influence of vaccination coverage on the dynamics of COVID-19 pandemic with the effect of environmental contamination, Math. Methods Appl. Sci. 46 (2023) 12425 - 12453, https://doi.org/10.1002/mma.9185.
[8] K. Sarkar, J. Mondal and S. Khajanchi, How do the contaminated environment influence the transmission dynamics of COVID-19 pandemic?, Eur. Phys. J. Spec. Top. 231 (2022) 3697 - 3716, https://doi.org/10.1140/epjs/s11734-022-00648-w.
[9] R. K. Rai, S. Khajanchi, P. K. Tiwari, E. Venturino and A. K. Misra, Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India, J. Appl. Math. Comput. 68 (2022) 19 - 44,
https://doi.org/10.1007/s12190-021-01507-y.
[10] S. Khajanchi, K. Sarkar and J. Mondal, Dynamics of the COVID-19 pandemic in India, arXiv preprint (2020) https://arxiv.org/abs/2005.06286.
[11] M. A. Khan and Fatmawati, Dengue infection modeling and its optimal control analysis in East Java, Indonesia, Heliyon 7 (2021) #e06023, https://doi.org/10.1016/j.heliyon.2021.e06023.
[12] S. He, Y. Peng and K. Sun, SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dyn. 101 (2020) 1667-1680, https://doi.org/10.1007/s11071-020-05743-y.
[13] M. A. Khan, A. Atangana, E. Alzahrani and Fatmawati, The dynamics of COVID-19 with quarantined and isolation, Adv. Difference Equ. 2020 (2020) #425, https://doi.org/10.1186/s13662-020-02882-9.
[14] A. J. Mumbu and A. K. Hugo, Mathematical modelling on COVID-19 transmission impacts with preventive measures: a case study of Tanzania, J. Biol. Dyn. 14 (2020) 748 - 766, https://doi.org/10.1080/17513758.2020.1823494.
[15] Y. A. Adebisi, A. Ekpenyong, B. Ntacyabukura, M. Lowe, N. D. Jimoh, T. O. Abdulkareem and D. E. Lucero-Prisno, COVID-19 highlights the need for inclusive responses to public health emergencies in Africa, Am. J. Trop. Med. Hyg. 104 (2020) 449 - 452, https://doi.org/10.4269/ajtmh.20-1485.
[16] BBC News, COVID-19 pandemic data/South Africa medical cases, BBC, Available at: https://www.bbc.com/news/world-asia-china, Accessed 25 July 2022.
[17] J. Kew, Covid-19 deaths pass 700,000; WHO to send 43 specialists to SA, BizNews, Available at: https://www.biznews.com/inside-covid-19/2020/08/05/covid-19-deaths, Accessed 26 July 2022.
[18] S. P. Gatyeni, C. W. Chukwu, F. Chirove, Fatmawati and F. Nyabadza, Application of optimal control to the dynamics of
COVID-19 disease in South Africa, Sci. Afr. 16 (2022) #e01268, https://doi.org/10.1016/j.sciaf.2022.e01268.
[19] M. L. Juga, Modelling the Ebola virus disease dynamics in the presence of interference of interventions, UJ. Master’s thesis, University of Johannesburg, South Africa, 2020.
[20] M. A. Khan, N. Ozdemir, I. Ahmad, N. M. Isa and E. Alzahrani, Modeling and analysis of HIV/AIDS spread in Pakistan: Role of optimal control and behavioral changes, J. Comput. Appl. Math. 473 (2026) #116913, https://doi.org/10.1016/j.cam.2025.116913.
[21] J. D. Murray, Mathematical Biology: I. An Introduction, Springer, New York, NY, 2007.
[22] C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng. 1 (2004) 361 - 404, https://doi.org/10.3934/mbe.2004.1.361.
[23] J. L. Salle and S. Lefschetz, Stability by Liapunov’s Direct Method: With Applications, Academic Press, New York-London, 1961.
[24] N. Chitnis, J. M. Hyman and 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, https://doi.org/10.1007/s11538-008-9299-0.
[25] M. A. Khan and 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.
[26] T. -M. Chen, J. Rui, Q.-P. Wang, Z.-Y. Zhao, J.-A. Cui and L. Yin, A mathematical model for simulating the phase-based transmissibility of a novel coronavirus, Infect Dis Poverty 9 (2020) #24, https://doi.org/10.1186/s40249-020-00640-3.
[27] D. McEvoy, C. McAloon, A. Collins, K. Hunt, F. Butler, A. Byrne, M. Casey-Bryars, A. Barber, J. Griffin, E. A. Lane, P. Wall and S. J. More, Relative infectiousness of asymptomatic SARS-CoV-2 infected persons compared with symptomatic individuals: a rapid scoping review, BMJ Open 11 (2021) #e042354, https://doi.org/10.1136/bmjopen-2020-042354.
[28] S. A. Lauer, K. H. Grantz, Q. Bi, F. K. Jones, Q. Zheng, H. R. Meredith, A. S. Azman, N. G. Reich and J. Lessler, The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: estimation and application, Ann. Intern. Med. 172 (2020) 577 - 582, https://doi.org/10.7326/M20-0504.
[29] B. Ivorra, M. R. Ferrández, M. Vela-Pérez and 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. Numer. Simul. 88 (2020) #105303, https://doi.org/10.1016/j.cnsns.2020.105303.
[30] Statistics South Africa, Stats SA, Available at https://www.statssa.gov.za/?p=16711#: :text.
[31] Worldometer, COVID-19 Coronavirus Pandemic, South Africa, Available at: https://www.worldometers.info/coronavirus/, Accessed 30 July 2024.
[32] X. Chen, Z. Huang, J.Wang, S. Zhao, M. C.-S.Wong, K. C. Chong, D. He and J. Li, Ratio of asymptomatic COVID-19 cases among ascertained SARS-CoV-2 infections in different regions and population groups in 2020: A systematic review and meta-analysis including 130, 123 infections from 241 studies, BMJ Open. 11 (2021) #e049752, https://doi.org/10.1136/bmjopen-2021-049752.
[33] C. Maslo, R. Friedland, M. Toubkin, A. Laubscher, T. Akaloo and B. Kama, Characteristics and outcomes of hospitalized patients in South Africa during the COVID-19 Omicron wave compared with previous waves, JAMA. 327 (2022) 583 - 584, https://doi.org/10.1001/jama.2021.24868.
[34] F. Wilta, A. L. C. Chong, G. Selvachandran, K. Kotecha and W. Ding, Generalized susceptible–exposed–infectious–recovered model and its contributing factors for analysing the death and recovery rates of the COVID-19 pandemic, Appl. Soft Comput. 123 (2022) #108973, https://doi.org/10.1016/j.asoc.2022.108973.
[35] Department of Statistics, South Africa, Protecting South Africa’s elderly, SSA, Available at: https://www.statssa.gov.za/?p=13445, Accessed 15 July 2023.
)