A scenario analysis for COVID-19 in South Africa

Ciaran Burks (6 Min Read)

Yesterday, on Sunday the 15^th of March, the President of South Africa – Cyril Ramaphosa – instituted measures that South Africans can and must take to contain the spread of the COVID-19 virus. Opinions on the virus, like many topical issues, are varied and often emotive. Talking heads range in their assessments of the situation. “Don’t Panic”, “Self-Isolate”, “We must slow the spread”, and “It can’t be contained” are a few phrases, so often repeated, that they already border on cliché.

What can we expect from Covid-19 in South Africa? How many cases will there be in 1 month? Are the measures instated by the President any help? These are some of the questions South Africans want answered.

What can we expect?

In order to understand what we should expect in South Africa, it is important to understand the virus’ behaviour in other geographies. Worldwide, both inside and outside of China, the virus has grown roughly 15% day-on-day. In other words, the number of new cases today is about 1.15 times the number of cases yesterday.

There are really three stages in the spread of a pandemic like Covid-19, and they can be described by mathematical relationships. The first stage – exponential growth – is detailed above. The graph above records cases of the Covid-19 virus outside of China since January. Cases grew at roughly 15% per day, resulting in an upward sloping exponential curve. The implication of such a curve is this: the rate of infections is increasing, meaning that within a matter of months, compounding leads to massive infections, at least if the rate of 15% is maintained. The nature of exponential growth, however, is that it must slow at some point, either as the entire population is already infected, or as quarantines limit the chance for new infections.

When should we expect the spread of Covid-19 to slow? China has managed this feat. The nation has managed to control the spread of the virus – for now – through extreme measures, seen through a flattening curve.

The data from China show the two steps that occur after exponential growth. It is possible to use China as an example since China is further along the curve than any other country. Here we see that China managed to move from exponential growth (an upward sloping curve where the rate of cases increases day by day) to a downward sloping curve (where there are still new cases, but this rate is not accelerating), in less than one month. After one month, it seems that China has managed to slow the rate down so much that even reaching 100,000 total cases will take some time. This is shown by the very mild slope at the end of the graph, which characterises the last phase of an epidemic – the slowdown.

How has China managed to achieve this remarkable slowdown? The control that China has on its people is unprecedented; the reaction by Chinese officials was swift and decisive and extreme quarantines limited the spread of new infections drastically. Enforced quarantines also mean that new cases are not being recorded, so this reported slowdown is sure to underestimate the number of new cases. It is unlikely that the rest of the world will be able to slow the spread of the virus as quickly as China. However, in a few weeks, we will be able to assess the numbers in Italy to determine if the country has managed to slow the virus down effectively with its extreme measures.

Possible Numbers for South Africa

If the measures announced by President Ramaphosa on Sunday are taken seriously by the public, South Africa may be able to slow down the spread of the virus significantly.

By slowing the rate of new infections early, through improved hygiene, self-isolation, the banning of large gatherings and other measures, South Africa could drastically limit the number of cases. The curve above represents a scenario with an average growth rate of 12%, but where early and effective measures lower the compounding rate as soon as possible. In this scenario, the infection rate is lowered to 9% by early April. At this point, the curve could do one of two things. It might continue growing at a reduced rate as shown in figure 3, or it might flatten. If quarantining measures are followed strictly, as in the case of China, and South Africans everywhere do everything in their power to limit the spread of the virus, then we may event start to see a flattening of the curve.

If the South African population is not careful and delays its response, leading to the now standard 15% infection rate through April, the numbers look very different. Figure 4 shows how exponential growth works for the virus. A delayed response will mean that – especially in the context of immuno-deficiency and struggling public healthcare – the virus is likely to infect more than 4 million South Africans by 30 May, and most South Africans by the end of the year. The number of deaths will then inevitably climb into the hundreds of thousands.

Is it even possible to contain COVID-19, and should we try?

There are many who argue that it would be best to forget about quarantining anyone, cancelling gatherings and merely continue business as usual. There is some credence to this claim, since it is extremely costly to prevent the spread of such an infectious virus. The key reason for slowing down the virus is explained in figure 5. Taking protective measures spreads out the number of cases, and helps the healthcare system to cope with those who are at the highest risk.