Long Term COVID-19 Forecasts for South Africa

by Richard Armstrong, Bruce Bassett, Nadeem Oozeer and Felix Silwimba; as part of the SARAO Data Science team's work for the National Ventilator Project.

"All models are wrong, but some are useful" - George Box, British statistician

Predicting deaths from COVID-19 is hard: in the first few days of June 2020, the disease had killed 45 people in Qatar but 9522 in Belgium, yet Qatar - with 62,160 infections - had about 3500 more cases than Belgium. That is a ratio of about 200:1 in deaths, yet both countries had tested about 80,000 people per million of the population.

Predicting future COVID deaths is hard; or as Koos Bekker recently opined about general COVID-19 forecasts, "Only mamparas will try to predict the outcome of catastrophes."

With this in mind how many deaths should we expect in South Africa, and how accurately do we think that anyone can predict the final death toll? There have been optimistic suggestions that the total number of deaths will be low: in particular claims of 59,300 (here), 48,000 here and 30,000-50,000 (here; though the latter, for example, included many caveats about unmodelled uncertainties). If these projections turn out to be true it would be great news given that early projections were that over 300,000 South Africans might die, so let's indeed hope they turn out to be correct.

Unfortunately unjustified hope can be negative. The low death forecasts may give the impression that COVID-19 is guaranteed to only kill a relatively small number of South African's no matter what the public or government do for the rest of 2020 and 2021. One might be tempted to argue that if less than 50,000 people are going to die no matter what, then why should one bother to social distance, wear a mask or work from home?

Instead in this blog post we will attempt to convince you that:

1. it is currently impossible to predict the final death toll with any accuracy, and
2. it is still very possible that there will be more than 100,000 total deaths in South Africa over the next two years from COVID-19. Further, the original 300,000+ death toll must still be considered a realistic possibility.

This is neither unexpected nor controversial, though somehow it feels like it given the current strong predictions in South Africa: Nassim Talib has written about this more generally where he says: "At the onset of the COVID-19 pandemic, many researcher groups and agencies produced single point “forecasts” for the pandemic... The prevailing idea is that producing a numerical estimate is how science is done, and how science-informed decision-making ought to be done: bean counters producing precise numbers. Well, no. That’s not how “science is done”, at least in this domain, and that’s not how informed decision-making ought to be done."

Before we get into serious modelling to back up our claims, let's start by addressing an argument that goes something like this:

"How can we expect over 100,000 deaths in South Africa when Italy/Spain/(insert your favourite 1st world country) have only had 34,000/27,000/etc... deaths and they have been hit much harder than us?"

The counter to this is straight-forward. First, South Africa is not a 1st world country and is no stranger to massive infectious disease death tolls: HIV deaths alone were estimated to exceed 250,000 a year for several years around 2006, and HIV is still a massive cause of death today. Further, our lockdown has not managed to bring the spread of the disease under control as it did in the first world: on 14th June we had the highest percentage of new cases in the world.

Second, let's wait and see what the total deaths in Italy/Spain/your favourite country are in January 2021 or 2022. History is full of sports matches where teams who were winning in the first quarter ended up losing badly by the end of the match. We simply don't yet know how long COVID-19 is going to be with us. It could be months if we develop effective treatments or a vaccine quickly, or it might last years if we don't. While the disease is with us, we should expect multiple waves of infections. As an example, have a look at daily cases in Iran who are just going through their second wave:

Iran is not alone in experiencing a 2nd wave: we must not forget just how extremely infectious COVID-19 is.

The fact that we don't really have any idea how long COVID-19 will be with us should already suggest that accurate long-term predictions are going to be difficult to make. If this sounds hard to believe, please reread the opening lines of this article and try to imagine predicting the Qatar and Belgium deaths today back in early March when both countries had less than 5 known cases each. As in this example, we will try to convince you that we cannot now predict the eventual number of deaths in South Africa that will occur over the next two years to better than about 50x. In other words, 10,000 and 500,000 deaths, and everything in between, are still possible final death tolls for South Africa due to COVID-19. Such long-tails are a known issue for epidemics.

This huge uncertainty is a bitter pill to swallow, so we invite you to stay critical, but open minded, while we work through the evidence.

Understanding the original predictions

First let's understand where the original predictions of around 300,000 deaths came from and why they are pretty robust.

Predicting final deaths for a disease is easy in principle: you just multiply the average Infection Fatality Rate (IFR; the probability of dying given infection) by the final total number of infections in the country: if 1 out of 100 people dies on average, and 100,000 people get infected, we would expect 1,000 people to die.

So how many infections should we expect in total in South Africa? The standard, simplistic, epidemiological answer to this is provided by the following curve which gives the final "herd immunity" fraction of infections in the population:

Figure 1: predicted fraction of population infected as a function of reproductive number, Rt. It predicts about 60% of the population will be infected if Rt = 1.5 and about 80% infections for Rt = 2.

Figure 1 links the proportion of the population who are expected to be infected given enough time to the reproductive number, Rt, a crucial quantity that we will need for all our forecasts. Rt is defined to be the average number of people an infected person will in turn pass the infection on to (think of John infecting Bob, Mary and Sizwe, yielding Rt = 3). It is important to note that the reproductive number is an average and that it changes with time, so it is useful to distinguish its initial value (R0 - when it starts spreading and no one knows about the disease) and its value at a later time, t, denoted by Rt. The value of R0 can be more than 10 for some diseases like the measles or mumps and is around 0.9-2.1 for influenza.

So for flu you usually infect just 1-2 other people but for COVID-19 R0 is estimated to be between about 2 and 6, so looking at Fig 1 we see that if nothing were done, we would expect at least 80% of any population to become infected with COVID-19 before the disease naturally stopped spreading, due to the fact that it becomes less and less likely that an infected person will come into contact with someone who has not had the disease yet (assuming that recovering from COVID-19 confers some immunity). For South Africa this would mean about 48 Million infections in the end.

Now, the great thing about being intelligent beings is that we humans can change our behaviour in response to a disease. We can educate ourselves, share advice, wear masks, wash our hands, stop kissing, practise social distancing and so on. This all has the effect of reducing Rt over time, which reduces the final numbers of infections. The problem is, unless it has eradicated the disease, as soon as a country goes back to "normal", the exponential spread of the disease returns (as in Iran) and we should expect to head towards the relevant herd immunity limit shown in Figure 1.

In the absence of a vaccine, it is hard to keep Rt much lower than R0 for long periods of time since this typically requires severe measures such as lockdown & closing of schools that have dire economic consequences. As a result, unless a country can eliminate the disease relatively quickly - as New Zealand currently appears to have done for example - they must expect a protracted dance with multiple waves of infections.

In South Africa we have so far not been able to achieve and sustain Rt < 1 (like many other developing countries but unlike most 1st world countries). As a result, eradicating the disease will be hard, though we hope not impossible. If we assume we can keep Rt to around 1.5, then we would predict about 60% of South Africa would get infected, i.e. around 36M people.

How many deaths will that cause? Well the Infection Fatality Rate (IFR) is still poorly known. In the early days the best data came from the Chinese CDC which found that about 2.3% of their positive test cases died. This is a worst-case scenario since there are many infections that are missed and not tested. Using the China CDC data leads to predictions for South Africa of about 4800 deaths per 1% of the population infected and hence about 288,000 deaths if 60% of South Africa were infected (Note that because of SA's young population only about 0.8% would die using the Chinese CDC Case Fatality Rates).

Fortunately we now know that the Infection Fatality Rate (IFR) is significantly less than 2.3% in general because of the large number of asymptomatic infections and infections that go undetected due to the limited testing capacity in most countries. Best estimates for the average IFR are now somewhere around 0.3%-1.4% with the lower limit coming from updated numbers from New York City, Madrid and Lombardy. Seroprevalence studies in Spain suggest that about 5.2% of the population have been infected, or about 2.4M people. Given that Spain has had about 27,000 confirmed deaths by mid June, this would put the average Spanish IFR at about 1.1%. Unfortunately this doesn't include missing untested deaths either directly or indirectly due to COVID-19, which could increase the IFR by up to 50%. In South Africa there is no sign yet of excess mortality but there is in the Western Cape.

What should we expect the South African IFR to be on average? There are a number of key points to consider:

1. South Africa's health care system has limited ICU facilities. If you really need ICU care and don't get it, the probability of survival is small. This has already been an issue in hard hit places like Italy, Spain and New York.
2. We have about 8M HIV infections, a high TB burden and a high proportion of hypertension, obesity and malnutrition. We do not know yet for sure how HIV or the others will affect the IFR for South Africa.
3. South Africa has a young population (only about 5% over 65 years of age) and young people typically have a significantly lower IFR than those over 70.

First world countries have a double advantage over developing countries when it comes to critical care: their lockdowns work more effectively, flattening the curve and reducing pressure on ICU facilities and they typically start with more ICU beds per capita and have greater capabilities to rapidly increase their numbers of ICU beds. South Africa has in the region of 3000-4000 ICU beds including both private and public hospitals. Even the moderate estimates predict peak ICU bed demand exceeding 20,000. Our models predict peak demand could hit 50,000+ which will push up the South African IFR significantly as we discuss later.

Preliminary data from the Western Cape shows that HIV is likely to be a significant factor in South African COVID-19 deaths, with a hazard ratio approximately double that of hypertension, which is a well-known major COVID-19 comorbid condition. For people under 50, HIV was the 2nd most common comorbidity after diabetes. Consider also infant deaths. So far the Western Cape already has 2 younger than five years old, while New York only had 4 deaths under 10 years of age in total out of more than 24,000 deaths.

The bottom line is that we really don't know what the final South African average IFR will be, even if we assume that there is only one important strain of COVID-19, which now looks less and less likely. That means that even if we knew the number of infections perfectly, we are not able to currently predict final deaths to within a factor of 2-3.

So now lets move on to the problem of predicting the final number of infections.

To make precise predictions we need to know our friend Rt for all times over the next year or two. One way to think of Rt is that it is the product of three terms: (1) the probability an infected person will infect someone in a single meeting, (2) the average number of people the infected person meets per day and (3) the number of days they are infectious. And we need to know these three factors for the next 12 months and beyond if we want to predict the total number of infections accurately. A tough ask...

To predict Rt accurately we would need to know what lockdown level the country will be in every month for the next 12 months and also how well the community will comply with the lockdown levels. Just because for example the government mandates a level 5 lockdown doesn't mean people will necessarily comply! Further, we need to know how much of a factor winter will be in the spread of the disease, how many infections we are missing due to limited testing, whether mask usage, contact tracing and quarantining will be effective, and whether there are other, more transmissible strains circulating. We also don't know if blood type will play a role, or whether people will have partial immunity due to previous exposure to the commonly circulating coronaviruses (the non-novel ones). None of these factors are known accurately now. So how should we proceed?

One approach could be to simply take our best guess at what Rt will look like for the next 12 months. That will certainly give us a precise total number of deaths, but should we believe the answer? I could tell you that you have 52,835,834 hairs on your head. That is a very precise answer but it is probably not at all accurate. One way to check is to make lots of reasonable guesses at Rt and see how much our final answers change. If they change a lot we probably shouldn't have much confidence in our guess. So let's do that. A few Rt curves might look like this:

Figure 2: 25 example curves for the evolution of Rt over the next year

We choose Rt to start around 1.3-1.6 (since that corresponds to April and May where we have observational data) and then allow it to jump up/down depending on whether one thinks that the lockdown level will go down/up, whether winter will have a big effect or masks will be widely used or be effective etc... Note that when Rt < 1, the daily cases are declining while when Rt > 1 implies that the daily infection numbers will increase (as they have since April to the current date, 12 June). Note that testing plays a crucial role here - if you reduce testing efficiency it may look like Rt < 1 even if, in fact, Rt > 1.

But this small number of scenarios doesn't give us enough feeling for the full range of possible futures. Instead, let's make 2000 such curves. Each one of them represents a possible future, a kind of parallel universe that we might find ourselves in over the next year that is consistent with our current uncertainties about COVID-19, the choices of the South African government and people over the next 12 months, etc...

Then we get something like this:

Figure 3: 2000 simulated Rt curves used for our ensemble over time. They include a death-dependent cutoff on Rt mimicking how people will naturally act in their own best interest as deaths increase, which is why the curves narrow down around 1 over time.

The white line represents the median value, while the yellow and black lines give the 68% and 95% limits across our 2000 simulations. Note that these 2000 models include a range of pessimistic (Rt > 2), "average" (1 < Rt < 2) and optimistic (Rt < 1) scenarios reflecting the unavoidable uncertainties about the future progression of the disease in South Africa. However, the relative balance between optimistic/average/pessimistic scenarios is not God-given: we still have to make a best guess about the range of possible Rt behaviours that can happen, and this moulds the range of scenarios. As time goes by we will learn whether they were appropriate. That is one of the reasons we have released the code: so you can put in your own beliefs and see what the implications are.

So what do these Rt curves predict? Each one can be run using a compartmental model which follows the flow of people from susceptible through infected and ending either recovered or dead. All the details are available in our report, but the main results are contained in this "horse-tail" plot:

Figure 4: 2000 simulations starting from 1 April 2020 (day 0) in South Africa and running until the end of March 2021, showing total cases and deaths, and numbers of critical & hospitalised. The white lines represent the median values at each time. The black line in the cumulative deaths (top right) shows the actual South African deaths to June 5. The plots are logarithmic with final deaths (on day 365) running from a few thousand to around 700,000.

Each panel shows 2000 curves, one for each Rt curve above, starting from 1 April (day 0) and running for 365 days, shown on a log scale.

The important features that you should take away from this plot:

1. There is a huge amount of uncertainty in all quantities: including the final number of deaths, the date and magnitude of the peaks in critical (ICU) and hospitalisation and the total number of infections.
2. Most of our models, starting from 1 April, under predicted the observed deaths in April, May and early June (see the black line in the top right panel). We discuss this more below.
3. The median number of final deaths in our simulations was about 140,000. That means half of our models ended up with more than 140,000 deaths.
4. A significant number of our simulations had a lot of deaths in the first three months of 2021. We must be careful not to let our guard down even if we have a good 2020.
5. Although there were a few percent of simulations with large numbers of deaths (over 400,000) there were also a few percent of simulations with less than 10,000 deaths, representing models in which we are able to bring Rt < 1 and keep it there. The range is very wide.

The latter point is broadly consistent with the CMMID analysis of Low and Middle Income Countries projection of 41,000 to 290,000 deaths in South Africa, though their range is somewhat smaller than ours since their treatment of Rt is significantly simpler.

One critical point, which is actually another manifestation of our main result, is that our range of deaths (from 3,000-700,000), and our median (140,000 deaths), are themselves sensitive to assumptions. Think that we have been too generous on the lower bound of the IFR? Then the lower estimate jumps up. Think that the range of infectiousness period or asymptomatic fraction are wrong? Then the upper bound jumps above 1M or below 400,000. This is all just more grist to the mill of uncertainty: forecasting is hard.

Let's quickly address the issue of why our simulations, starting from 1 April, are mostly under predicting actual South African deaths in April, May and June in Figure 4. Below is the distribution of IFR values in our 2000 simulations both with (red) and without (black) explicit modelling of ICU overwhelm.

25% of scenarios had an IFR < 0.2% in the no-ICU overwhelm case. Given that HIV appears to be a significant comorbidity for COVID-19 it is likely that this range of IFR values is actually excluded in South Africa. Or it may be a transient effect, driven by our assumptions about Rt which are too tightly constrained at early times, or it may be that we have more undetected cases than our simulations allow for. It is something we will keep track of over the next few weeks, but doesn't affect our main conclusions.

Perhaps you are skeptical about all studies predicting large numbers of deaths or large uncertainties for South Africa? Part of our high numbers are driven by the current uncertainties about the properties of the disease, part by ICU overwhelm (which we discuss below) and part by uncertainties about Rt, as we discussed above. Let's briefly chat about the first issue. There are a lot of parameters that go into making a prediction: a lot have to do with severity: the fraction of asymptomatic patients, the percentage of patients who will be tested, the percentage of patients who will need hospital treatment etc... But there are other key unknown parameters such as the length of time someone is infectious, which plays a crucial role in determining Rt.

Part of the problem is that available studies are often contradictory, because they are often based on small samples. It is therefore important to allow for the full range of our current uncertainty when making forecasts, not just to cherry pick the results that best fit a particular narrative. For example, some studies assume the asymptomatic fraction to be around 75%. But the comprehensive analysis of the town of Vo' in Italy, where everyone was tested twice, found an asymptomatic fraction around 43%. Assuming 43% for the asymptomatic fraction instead of 75% pushes up predicted deaths significantly. We deal with such uncertainties by also allowing the key parameters to vary within our best estimates of their current uncertainty ranges, but sensible, knowledgable people can disagree on what those ranges are.

It is also critical to appreciate that parameter estimates are often subtly dependent on testing. For example, the fraction of cases needing hospitalisation is often taken to be around 20%, the number found in China. But this fraction is much higher or lower in countries that test less/more per capita than China. In the extreme case, if you only test very severe cases you will, instead, find that nearly 100% need hospitalisation. So if you are in a country that only tests the most severe cases using a 20% hospitalisation fraction will lead to a significant under prediction of deaths.

This is all quite abstract so let's consider a couple of specific toy examples. By "toy" here we mean straw man scenarios that are not realistic models of South Africa but which capture some useful insights. These will provide some intuition about where the high death numbers are coming from.

We will compare four toy scenarios for South African covering two years from April 2020 to March 2022. The first scenario has Rt = 1.05 at all times. This mimics a very strict lockdown that lasts for 2 years. It leads to only about 10,000 deaths, though that number is still increasing after two years as the disease continues to spread slowly through the population. The other three scenarios also all start with Rt = 1.05 but then transition to Rt = 2 after 6, 12 and 18 months respectively. This mimics coming out of lockdown and returning to something like "normal" life. What is notable is that all the three scenarios end up with the same number of deaths: about 470,000, as shown in the figure below.

Figure 5: Deaths over time from 1 April 2020 in four toy scenarios. The first (bottom curve) with Rt = 1.05 for two years, the other three scenarios start with Rt = 1.05 but transition to Rt = 2 after 6, 12 and 18 months (at the grey vertical lines). All of these latter three end with the same number of deaths of about 470,000, independent of when the lockdown ended showing that countries need to be vigilant over long time scales.

Why doesn't it matter when the lockdown happens in terms of determining the final death toll? Why does't all that hard work for 6, 12 or 18 months count for anything in the end? Well, remember Figure 1? It said that the only thing that mattered in predicting the final infection fraction was the value of Rt. In this case, the most important value was the phase with Rt = 2, which in this toy model case predicts that 80% of South Africa would become infected, and hence that there would be very high numbers of deaths.

Referring to Figure 1 isn't really an explanation of why the long initial lockdown makes no difference though. So consider this one instead: COVID-19 may have started spreading in 2019 or perhaps it could have been 2014 or 1998. What matters is when it mutated to become highly transmissible (where Rt is much larger than 1) and that appeared to happen late in 2019. In the same way, it doesn't matter when Rt is small (1.05 in the above scenarios), it only matters when Rt reaches its highest values.

A final analogy might help clarify this important point. Imagine you decide to shoot yourself at midnight tonight but at 11:45 a friend calls you and spends 45 minutes trying to convince you not to. But at 12:30 you hang up and shoot yourself anyway. What did that phone call ("lockdown") buy you? Nothing really - it just delayed the shooting by 30 minutes. In the same way, 18 months of forbearance essentially buys nothing if the lockdown is then released while infections are still spreading. What matters is the maximum value of Rt. If it cannot eradicate the disease then South Africa needs to try to achieve the lowest Rt value that it can afford to sustain over a long period until a vaccine is available. This is not going to be quick, not for South Africa and not for most countries.

An important factor in our pessimistic scenarios where we see a large number of deaths is our modelling of ICU overwhelm; basically demand outstripping supply when it comes to ICU beds. So let's have a brief discussion of what effect South Africa's limited ICU facilities has on fatalities.

ICU Overwhelm

South Africa has somewhere in the region of 4000 ICU beds in private and public hospitals. Looking at Figure 4 we see that the peak numbers in critical state (i.e. needing ICU) typically exceed 30,000. At peak only the youngest and healthiest people will be given ICU access. We assume their fatality rate will be around 30% while for the rest their prospects are unfortunately very poor. In Figure 4 we allow it to vary between about 50 and 95% but for concreteness here we assume it is 85%.

To see what effect this has on fatalities let's take our last scenario, the one that starts with Rt = 1.05 and transitions to Rt = 2 after 180 days, but in the one case we assume everyone has access to an ICU if they need it while in the other only 4000 people have access to ICU at any time. The differences are stark. In the case with no ICU overwhelm only about 210,000 die. When we include ICU overwhelm it rises back to 470,000. Germany's relatively low death rate likely is partly due to their high number of ICU beds per capita relative to Italy, Spain and the UK.

Figure 6 - In this toy model, ICU overwhelm more than doubles fatalities compared to a model without ICU overwhelm (Rt = 1.05 for 6 months followed by Rt = 2 for the remaining 18 months).

Unfortunately our conclusion is that ICU overwhelm is likely to significantly increase South Africa's IFR. In Figure 4 it increases the median number of deaths by approximately half. However, the goal of the National Ventilator Project is to reduce the number of people who need ICU.

The National Ventilator Project

The National Ventilator Project, managed by SARAO, has the goal of supporting South Africa's COVID-19 response via the large-scale production of non-invasive ventilators. The aim is to reduce the number of people who end up in ICU. We don't yet know how effective this approach will be but let's take our previous toy model and explore the effect of the non-invasive ventilators by assuming they change the fraction of hospitalised patients who end up in ICU in three scenarios: (1) the default value (25%), (2) 17% and (3) 12%. We assume only 4000 ICU beds, so there are extra fatalities from ICU overwhelm.

Figure 7 - the potential effects of non-invasive ventilators on critical cases and fatalities, in our toy model shown on a logarithmic scale. Keeping people out of the critical state is very effective at reducing deaths.

The results are shown in Figure 7 on a log scale which makes the differences look small but the critical ICU peak for these three toy scenarios changes from 72,000 to 48,000 to 34,000 (top left) which translates into final fatalities of 470,000, 309,000 and 206,000 respectively (top right), showing that investing in non-invasive ventilators may have a massive impact on reducing deaths even in the presence of ICU overwhelm if they can reduce the probability of people transitioning from general wards to high and critical care. Further, such interventions help reduce deaths even in the optimistic scenarios. Note in Figure 7 that there is no change in the total number of cases (bottom right), and only a small change in the number of hospitalised cases (bottom left).

Of course, our toy projections are overly hopeful, even if the non-invasive ventilators are very effective. Figure 4 shows that many of our scenarios have more than 300,000 people requiring hospitalisation at peak. South Africa only has about 100,000 hospital beds (an effect we have not modelled which will further increase fatalities over what we have projected) and even making 50,000 non-invasive ventilators will be a huge undertaking.

Conclusions

To summarise our main result: there are scenarios consistent with what we currently know about COVID-19 that have less than 10,000 total deaths, but equally there are scenarios with 400,000 or more total deaths. The future is not yet written: in the absence of vaccine or treatment breakthroughs, what the government and public do over the next 12-18 months will have a huge impact - positive and negative - on the final death toll.

However, the fact that many of our scenarios have high COVID-19 death tolls does not mean we are suggesting that lockdown should necessarily be reimposed or tightened. The hard tradeoffs between COVID deaths, damage to the economy, and the suffering and deaths directly or indirectly caused by strict lockdown are incredibly complex and far beyond the scope of our analysis. But let us not enter into those important discussions with a false sense of security about the worst-case COVID-19 scenarios.

Finally, you might argue that the compartmental models we have used are not sophisticated enough to accurately model the pandemic in South Africa and the world. Absolutely. They are relatively simple models. But more complex and realistic models must out of necessity have many more unknown knobs, levers and parameters that we don't know or can't know yet, and that extra flexibility will lead to even more uncertainties in the long-term pandemic predictions, so going to a more realistic model will not change our main results. It is like accurate long-term weather forecasting: it's just beyond our capabilities currently. For while I may hope that the weather will be 25C and sunny at 10am on 1 December from six months out, but I won't believe anyone who claims they can predict it with any confidence.

In the spirit of reproducible research we have also implemented our SEIR-HCD model as a Google Colab notebook which we encourage you to play with. Our report with full technical details, and discussion of limitations and next steps, is available here.

"All models are wrong, but some are useful" - George Box.