LETTER TO EDITOR
Year : 2020  Volume
: 13  Issue : 5  Page : 235236
Mathematical modelling of COVID19 in South Africa
Aroonkumar Beesham Department(s) and institution(s) Faculty of Natural Sciences, Mangosuthu University of Technology, P O Box 12363, Umlazi 4026, South Africa
Correspondence Address:
Aroonkumar Beesham Department(s) and institution(s) Faculty of Natural Sciences, Mangosuthu University of Technology, P O Box 12363, Umlazi 4026 South Africa
How to cite this article:
Beesham A. Mathematical modelling of COVID19 in South Africa.Asian Pac J Trop Med 2020;13:235236

How to cite this URL:
Beesham A. Mathematical modelling of COVID19 in South Africa. Asian Pac J Trop Med [serial online] 2020 [cited 2021 Jul 24 ];13:235236
Available from: https://www.apjtm.org/text.asp?2020/13/5/235/283519 
Full Text
The first case of coronavirus disease 2019 (COVID19) in South Africa arose when a group of people returned from Milan, Italy to Durban, South Africa on 1 March 2020. One person from this group was confirmed with COVID19 on 5 March 2020. Since then, the number has increased steadily as shown in [Figure 1][1]. On 15 March, the President of South Africa declared a national disaster. Gradually, flights to and from South Africa were curtailed, and the public was urged to practice social distancing. Then, on 27 March 2020, a national lockdown commenced with various restrictions, lasting 21 days. Following Sookaromdee and Wiwanitkit[2], an attempt is made to build a mathematical model for the spread of COVID19 in South Africa. Due to the large number of variables involved, and various uncertainties, we have adopted a very simple approach just to get a handle on the situation.{Figure 1}
Up to the time of the lockdown, 27 March 2020, the increase was growing exponentially [Figure 2]A. A good fit to the data is the equation y = axbecx, with a = 1.835 83, b = 0.349 009, c = 0.244 957 (R2 = 0.991 4). The restrictions since lockdown from 27 March 2020 have appeared to work very well, and since then, the increase has dropped to a linear fit [Figure 2]B: y = ax + b, with a = 55.274 7, b = 1 088.69 (r = 0.004 6). What are the reasons for this drastic drop in the increase? All persons were to stay at home, except for people in key positions, such as the police, essential shops, petrol stations and banks. In addition, South Africans were prohibited from travelling, especially overseas, and no flights were allowed to come in from outside the country. Therefore, contact between susceptible and infected persons has been minimised.{Figure 2}
It is interesting to speculate about what will happen in the future. Obviously this is a very difficult task, given the number of variables involved. One way is to join the two functions in a piece wise manner. If we try to find a “best fit” to all the data, we come up with [Figure 2]C, with the equation of the curve being the same as for that in [Figure 2]A, but with the parameters a = 257 562 χ 1010, b = 8.138 68, c = 0.246 673 (R2 = 0.989 1). What is most interesting will be how we respond after lockdown, and if the lockdown is extended.
On 13 April 2020, the total number of cases in South Africa stood at 2 272. In [Figure 1], we have plotted the accumulated number of cases per day in a line graph. The total number of deaths stood at 27, and the total number of deaths over time is shown in a line graph in [Figure 2]D. The total number of recoveries on 13 April 2020 stood at 410. It should be noted that we have only tested at the rate of 1 411 persons per million of the population. Once testing is done more widely, it is expected that the numbers of infected people will rise.
Conflict of interest statement
The author declares that there are no conflicts of interest.
Acknowledgements
The author is grateful to Jacques Cloete, University of Zululand, South Africa for assistance with the graphs, and to an anonymous referee for useful comments which led to an improvement in the article.
Author’ s contributions
A.B. conceptualized and designed the work, made data collection, data analysis and interpretation, also drafted the article, did critical revision of the article, and approved the final version to be published.
References
1  COVID19 Corona Virus South African Resource Portal. COVID 19 statistics in South Africa 2020. [online]. Available from: https:// sacoronavirus.co.za/ [Accessed on 13th April 2020]. 
2  Sookaromdee P, Wiwanitkit V. Imported cases of 2019novel coronavirus (2019nCoV) infections in Thailand: Mathematical modelling of the outbreak. Asian Pac J Trop Med 2020; 13(3): 139140. 
