COVID-19 Dynamics in Africa Under the Influence of Asymptomatic Cases and Re-infection

Subject Areas : International Journal of Mathematical Modelling & Computations

Abayomi Oke ¹ , Oluwafemi Bada ² , Ganiyu Rasaq ³ , Victoria Adodo ⁴ , Belindar Juma ⁵

1 - Department of Mathematics and Actuarial Science,
2 - Department of Mathematics, University of Benin, Nigeria
3 - Department of Mathematical Sciences, Adekunle Ajasin University, Nigeria
4 - Department of Mathematical Sciences, Adekunle Ajasin University, Nigeria
5 - Department of Mathematical and Actuarial Science, Kenyatta University, Kenya.

Received: 2021-04-02 Accepted : 2021-09-08 Published : 2022-03-30

Keywords: COVID-19, Reproduction Number, Coronavirus, re-infections, asymptomatic case detection,

Abstract :

Since December 2019 that the coronavirus pandemic (COVID-19) has hit the world, with over 13 million cases recorded, only a little above 4.67 percent of the cases have been recorded in the continent of Africa. The percentage of cases in Africa rose significantly from 2 percent in the month of May 2020 to above 4.67 percent by the end of July 15, 2020. This rapid increase in the percentage indicates a need to study the transmission, control strategy, and dynamics of COVID-19 in Africa. In this study, a nonlinear mathematical model to investigate the impact of asymptomatic cases on the transmission dynamics of COVID-19 in Africa is proposed. The model is analyzed, the reproduction number is obtained, the local and the global asymptotic stability of the equilibria were established. We investigate the existence of backward bifurcation and we present the numerical simulations to verify our theoretical results. The study shows that the reproduction number is a decreasing function of detection rate and as the rate of re-infection increases, both the asymptomatic and symptomatic cases rise significantly. The results also indicate that repeated and increase testing to detect people living with the disease will be very effective in containing and reducing the burden of COVID-19 in Africa.

References:

[1] D. Aldila, S. H. A. Khoshnaw, E. Safitri, Y. R. Anwar, A. R. Q. Bakry, B. M. Samiadji, D. A.
Amugerah, M. Farhan, I. D. Ayulani and S. N. Salim, A mathematical study on the spread of COVID-
19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia, Chaos,
Solitons & Fractals, 139 (2020) 110042.
[2] S. Annas, M. I. Pratama, M. Rifandi, W. Sanusi and S. Side, Stability analysis and numerical
simulation of SEIR model for pandemic COVID-19 spread in Indonesia, Chaos, Solitons & Fractals,
139 (2020) 110072.
[3] O. I. Bada, A. S. Oke, W. N. Mutuku and P. O. Aye, Analysis of the dynamics of SI-SI-SEIR avian
influenza A(H7N9) epidemic model with re-infection, Earthline Journal of Mathematical Sciences,
5 (1) (2021) 43–73.
[4] J. Carr, Applications of Centre Manifold Theory, Springer, New York, (1981).A. S. Oke et al./ IJM2C, 12 - 01 (2022) 37-49. 49
[5] C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1 (2) (2004) 361–404.
[6] CDC, Covid-19 dashboard, (2020).
[7] I. Cooper, A. Mondal and C. G. Antonopoulos, A SIR model assumption for the spread of COVID-19
in different communities, Chaos, Solitons & Fractals, 139 (2020) 110057.
[8] R. Derwand and M. Scholz, Does zinc supplementation enhance the clinical efficacy of chloroquine/hydroxychloroquine to win today’s battle against COVID-19?, Medical Hypotheses, 142
(2020) 109815.
[9] K. Hamizi, S. Aouidane and G. Belaaloui, Etoposide-based therapy for severe forms of COVID-19,
Medical Hypotheses, 142 (2020) 109826.
[10] R. I. Horowitz and P. R. Freeman, Three novel prevention, diagnostic, and treatment options for
COVID-19 urgently necessitating controlled randomized trials, Medical Hypotheses, 143 (2020)
109851.
[11] D. S. Hui, I. E. Azhar, T. A. Madani, F. Ntoumi, R. Kock and O. Dar, The continuing 2019-nCoV
epidemic threat of novel coronaviruses to global health - The latest 2019 novel coronavirus outbreak
in Wuhan, China, International Journal of Infectious Diseases, 91 (2020) 264–266.
[12] B. Ivorra, M. R. Ferrandez, M. Vela 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, Communications in Nonlinear Science and Numerical Simulation, 88 (2020) 105303.
[13] J. P. LaSalle and S. Lefschetz, The Stability of Dynamical Systems, SIAM, Philadelphia, (1976).
[14] Y. Li, B. Wang, R. Peng, C. Zhou, Y. Zhan, Z. Liu, X. Jiang and B. Zhao, Mathematical modeling and
epidemic prediction of COVID-19 and its signifcance to epidemic prevention and control measures,
Annals of Infectious Disease and Epidemiology, 5 (1) (2020) 1052.
[15] K. Liang, Mathematical model of infection kinetics and its analysis for COVID-19, SARS and MERS,
Infection, Genetics and Evolution, 82 (2020) 104306.
[16] M. Moore, B. Gelfeld and A. Okunogbe, Identifying future disease hot spots: infectious disease
vulnerability index, RAND Health Quarterly, 6 (5) (2017).
[17] NCDC, First case of corona virus disease confirmed in Nigeria, (2020).
[18] F. Ndairou, I. Area, J. J. Nieto and D. Torres, Mathematical modeling of COVID-19 transmission
dynamics with a case study of Wuhan, Chaos, solitons, and fractals, Advance online publication,
135 (2020) 109846.
[19] M. K. Njenga, J. Dawa, M. Nanyingi, J. Gachohi, I. Ngere, M. Letko, C. F. Otieno, B. M. Gunn
and E. Osoro, Why is there low morbidity and mortality of COVID-19 in africa?, The American
Journal of Tropical Medicine and Hygiene, 103 (2) (2020) 564–569.
[20] A. S. Oke. Convergence of Differential Transform Method for Ordinary Differential Equations,
Journal of Advances in Mathematics and Computer Science, 24 (6) (2017) 1–17.
[21] A. S. Oke and O. I. Bada, Analysis of the dynamics of avian influenza A(H7N9) epidemic model
with re-infection, Open Journal of Mathematical Sciences, 3 (2019) 417–432.
[22] A. S. Oke, O. I. Bada, G. Rasaq and V. Adodo, Mathematical analysis of the dynamics of COVID-19
in Africa under the influence of asymptomatic cases and re-infection, Mathematical Methods in the
Applied Sciences, 45 (2022) 137–149.
[23] D. Okuonghae and A. Omame, Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria, Chaos, Solitons & Fractals, 139 (2020) 110032.
[24] P. K. Raghav and S. Mohanty, Are graphene and graphene-derived products capable of preventing
COVID-19 infection?, Medical Hypotheses, 144 (2020) 110031.
[25] M. Ruth, Africa braces for coronavirus, but slowly, The New York Times, (2020).
[26] S. Salehi, A. Abedi, S. Balakrishnan and A. Gholamrezanezhad, Coronavirus disease 2019 (COVID-
19): A systematic review of imaging findings in 9191 patients, AJR. American Journal of Roentgenology, 215 (1) (2020) 87-93.
[27] K. Sarkar, S. Khajanchi and J. J. Nieto, Modeling and forecasting the COVID-19 pandemic in India,
Chaos, Solitons & Fractals, 139 (2020) 110049.
[28] S. Seifirad, Pirfenidone: A novel hypothetical treatment for COVID-19, Medical Hypotheses, 144
(2020) 110005.
[29] F. Taghizadeh-Hesary and H. Akbari, The powerful immune system against powerful COVID-19: A
hypothesis, Medical Hypotheses, 140 (2020) 109762.
[30] A. D. Toit, Outbreak of a novel coronavirus, Nature Reviews Microbiology, 18 (3) (2020) 123–123.
[31] O. Torrealba-Rodriguez, R. A. Conde-Gutierrez and A. L. Hernandez-Javier, Modeling and prediction of COVID-19 in Mexico applying mathematical and computational models, Chaos, Solitons &
Fractals, 138 (2020) 109946.
[32] P. Van Den Driessche and P. J. Watmough, Reproduction numbers and sub-threshold endemic
equilibrium for compartment methods of the disease transmission, Mathematical Biosciences, 180
(2002) 29–48.
[33] J. Wang, Mathematical models for COVID-19: applications, limitations, and potentials, Journal of
Public Health and Emergency, 4 (2020), doi:10.21037/jphe-202.
[34] N. Wang, Y. Fu, H. Zhang and H. Shi, An evaluation of mathematical models for the outbreak of
COVID-19, Precision Clinical Medicine, 3 (2) (2020) 85–93.
[35] WHO, Covid-19 cases top 10,000 in africa, (2020).
[36] 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.
[37] C. Yang and J. Wang, A mathematical model for the novel coronavirus epidemic in Wuhan, China,
Mathematical Biosciences and Engineering, 17 (3) (2020) 2708–2724.
[38] Y. Zhang, X. Yu, H. G. Sun, G. R. Tick, W. Wei and B. Jin, Applicability of time fractional
derivative models for simulating the dynamics and mitigation scenarios of COVID-19, Chaos, Solitons
& Fractals, 138 (2020) 109959.