In the early stage of the coronavirus outbreak, the spread of the virus is essentially a random branching process. For example, one infected person can give the virus to 3 other people. Those three people each give it to two or three more. Now another nine people have it, and they pass it on and on. The number of cumulative confirmed cases could skyrocket to more than 7 million in just two weeks. This compounding effect is known as exponential growth.
It is exactly what is happening in Australia right now – the virus itself spreads exponentially. On 1st March, Australia only had 29 confirmed cases. By 30th March, the number had grown to more than 4000!
You might think it’s a tiny fraction of the country’s population (over 25 million). Well, that is just linear thinking. With a population of 24.28 million as of 2019, Shanghai only has less than 500 confirmed cases so far. This is the city that ranks first in China and 5th in the world in terms of population, and it has an average population density of 2,059 people per square kilometre. What is the population density in Australia? 3 per square kilometre!
So, how bad will the coronavirus outbreak get in Australia?
With exponential growth, the number of new cases each day goes up really fast. Graph the total over time in Figure 1, and you can see that the line curves upward at an increasing rate.
A different way to chart the spread of the coronavirus is to put the y-axis on a logarithmic scale (base=10). Now the red skyrocketing curve shown in Figure 1 transforms into a straighter curve in the figure below.
Presented in this way, the data clearly shows that it took only about 10 days to go from 100 to 1,000 cases while it took more than one month to go from 10 to 100 cases. Of course, it might just reflect more widespread testing has been conducted within Australia.
Fortunately, no virus can spread at an exponential rate forever. Once a large number of people have become infectious, the probability of a confirmed case contacting another declines. This is simply because each person with the virus is exposed to a random subset of the population and at some point, most people they are exposed to will already be sick and cannot become new cases.
Hence, over time the growth rate will slow down and we will end up with a curve like this, which is called “logistic growth”. Then the exponential growth just becomes the beginning of a logistic curve.
The height of any point on the logistic curve shows us how many total cases as of that day, but if we take the slope at that point, then we will get the number of new cases on that day: not too many cases early on but then a lot on each day and then fewer new cases again as the virus dies out.
The point where this curve goes from curving upward to instead curving downward is known as the infection point, which separates the curve into two regions of opposite concavity. At this point, the number of new cases each day, represented by the slope of this curve, is roughly constant and will soon start decreasing.
Plotting the different slopes along the logistic curve, we can get the graph (see below) that has drawn the most attention from our health experts. As the growth rate peaks and then begins to fall, the exponential curve gives way to a normal distribution. The bell curve refers to the projected number of infections during the pandemic.
The red bell curve above shows what a rapid outbreak looks like – when there is no protective measure to slow the number of new infections, a lot of people will get sick in a short amount of time and the mortality will explode. This is what health experts fear the most that a sudden explosion of illness will overwhelm the capacity of our healthcare system.
In Australia, we have just over 2,200 intensive care beds, with almost half of these in NSW. That’s around 8.9 ICU beds per 100,000 people which is even worse than Italy (12.5), where the virus has already overwhelmed their hospitals. If the virus infects 20-25 per cent of Australians as state departments are preparing for, there would be more patients than the number of beds available by early April. If that’s true, Australia would see a situation just like Italy, where doctors are forced to make heartbreaking decisions about WHO GETS TO LIVE on a daily basis.
However, when early and drastic control measures are imposed, the rate of new cases is slowed. By “flattening the curve” in this way, the number of severe cases will be spread out over a longer period of time, giving health professionals a reasonable chance to treat all patients with the available resources. To put it another way, if these two curves represent the same total number of people that eventually get sick, more people will die in the rapid outbreak scenario, because there won’t be enough hospital beds, medicine or ventilators available to keep them alive.
In 1918, the city of Philadelphia ignored warnings of influenza among soldiers preparing for WWI and held a parade attended by 200,000 people. Three days later, every bed in Philadelphia’s hospitals was full, and 4,500 people died within a week. A different story played out in St. Louis though. Within two days of detecting its first cases, the city closed schools, playgrounds, and even churches. Work shifts were changed. Public gatherings of more than 20 people were also banned. This was the result – a tale of two cities.
We’ve learnt from history that these extreme measures adopted in St Louis worked, which are now known as social distancing. There have been success stories to countries like China, South Korea and Singapore that have brought their outbreaks under control by implementing a combination of testing and social distancing. That’s why we often hear our health experts calling for drastic and rapid responses in the early days of a pandemic like COVID-19, when infection numbers are still relatively small.
Imagine, in our original example, A didn’t go out for lunch, B didn’t visit their mum, and C didn’t go to the Bondi Beach. The total number of infected cases would be dramatically reduced and so is the pressure on our doctors and nurses. When there is no vaccine or specific drug available, social distancing can make a huge difference between life and death. Hence, if more and more people start practising social distancing, the total number of infections could fall by several orders of magnitude, making the exponential growth work for us.
However, the success of the fight against the coronavirus relies to a remarkable degree on just one thing, that is whether individual Australians can follow official advice and stay at home. If eight out of ten Australians comply with strict social distancing measures, the curve will go down dramatically over the course of 4 months. If nine out ten do it, the curve will fall even faster, and then the duration could be as short as 13-14 weeks. Conversely, if just one person leaves their home when they don’t have to, we would expect the massive disruption to last way much longer.
Every individual Australian should step up and play their part because it only takes one person to put the rest at risk. We need to act on our responsibility to stay at home in order to break the person-to-person transmission of the virus, which is causing the absolute medical and economic disaster elsewhere in the world right now.
We have to be aware that the safest place for ourselves in a pandemic that is rapidly spreading through our communities is nowhere but home. We need to be psychologically prepared for the possibility that we might have to go through a long-term disruption to avoid a rebound in transmission.
We need to understand we are doing this with good intentions: to keep ourselves safe, to keep our loved ones safe, to keep the vulnerable safe, and to protect the frontline healthcare workers who are constantly working to keep us all safe. We are the solution, but we can also be the cause of more pain. So please listen to the advice of experts and stay at home. If you have not yet been following this advice, now is the time to do so before it’s too late.
I know it’s really hard to feel like you are saving the world when you are watching Netflix on your couch, but if all of us do the right thing, which is to practise social distancing, there shouldn’t be a big peak of infections afterwards.
Do you still remember this chart?
Well, it seems that the blue curve started bending downward since 24th March (see green points), which suggests that the rate of increase is slowing. This is largely due to the imposition of social distancing measures by the federal government and the states!
There you go. We are the solution. We must be together. ▲