More testing will give us a better picture of the coronavirus spread and its slowdown


Haydar Demirhan, RMIT University

Many states are now ramping up the number of tests by relaxing the criteria for who can get tested for COVID-19. This should give us a better idea of whether the spread is easing or getting worse.

We get regular updates about COVID-19 with lots of data, figures and graphs with some interpretations to see if we are flattening the curve on the number of new cases.

But most of these are based on using only the total or the daily number of confirmed new cases.




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This does not provide enough information about whether the situation is improving, stabilising or getting worse. That is why we also need to consider the number of people tested daily for COVID-19.

For example, in percentage terms there is no actual difference between getting 20 positive cases out of 1,000 tests one day and 100 positive cases out of 5,000 tests the next. Both lead to the conclusion we have 2% reported infected people of those tested.

If we are only given the number of new cases, getting 100 in a day sounds a lot worse than getting 20. The 2% percentage figure here tells us things are pretty much the same over the two days.

Curves and trends

Take Victoria, if we look at the total number of confirmed cases we see it followed an exponential trend for a while – one that was increasingly rising – and then started to divert on April 3.



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In the daily number of confirmed cases we see high jumps and large fluctuations going back and forth.



The Conversation, CC BY-ND

When the daily number of applied tests is considered, we can calculate the actual percentage of new cases each day. Now we have a way flatter curve (below) with different fluctuations.



The Conversation, CC BY-ND

The peak is now on March 24 when the number of tests is included. If we just look at the daily count, the highest number of confirmed cases was on March 27. When we look at the percentage, it shows a decrease rather than an increase with more than 2,300 tests.

From the daily new cases data it looks like there is a strongly decreasing trend in the number of confirmed cases between April 2 and 6.

But we do not see the same strong downward movement in the percentage data on the number of tests. Although both figures go down, then up slightly, the percentage trend downward is not as strong as the daily trend.

This is a good example of the discrepancy between the inferences from the raw and percentage data. When we consider the number of tested people, we get a different view on the progress of the pandemic.

More tests needed

In using the number of tests to get a more reliable picture of the situation, there is an important point to consider. That’s were the purple error bars in the graph (above) come in.

They show the margin of error where each percentage estimate swings for the daily number of applied tests, so the actual number could be higher or lower but within those purple bars.

When we have a larger number of applied tests, we get a reduced margin of error, and that gives us a clearer picture of what is happening.




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Since the peak on March 24 is backed up by only 500 tests, it has the largest margin of error. The figure on March 28 is based on 8,900 tests with a very small amount of error.

To get a more reliable picture of the situation, the number of applied tests has to be expanded, which it is what is happening in some states. This should reduce the margin of error.

Out in the community

After getting some signals of flattening the curve in Victoria and Australia as well, do we see an exponential increase in just the community transmission?

Community transmission is where someone has caught the virus locally, not an infected traveller who’s returned from a cruise or overseas. At the moment they are the minority of cases and authorities would like it to stay that way to contain the spread of the virus.

Again, we need to consider the number of tests to answer this question clearly. The raw numbers of community transmission in Victoria looked like they were increasing exponentially.



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But the numbers as a percentage of the number tested tell a different story. Although there is some increase in the rate of community transmissions recently, it still shows a way flatter behaviour far from the exponential curve.



The Conversation, CC BY-ND

That is why it is important to understand the impact of the number of tests on the figures displaying the progress of the pandemic. Understanding this relationship could reassure people about new numbers.The Conversation

Haydar Demirhan, Senior Lecturer in Analytics, RMIT University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Government says Australia’s coronavirus curve may be flattening


Michelle Grattan, University of Canberra

The federal government says there are signs the coronavirus curve may be flattening in Australia.

Scott Morrison told a Sunday news conference the rate of increase in cases had fallen to about 13-15% a day over the last few days, compared with 25-30% a day this time last week.

Health Minister Greg Hunt highlighted these numbers as “positive early signs of flattening of the curve”.

Hunt said there was much more work to do, but by people isolating and social distancing, “Australians are rising magnificently to this challenge”.

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But Victoria’s chief health officer Brett Sutton tweeted on Saturday, after pictures of many people at the beach, “Some of the behaviour today – when we’re asking people to stay home – has been really crap.

“It’s hard to change habits and it’s hard to see dangers that aren’t apparent yet. But with 3,000 cases of COVID in Australia this week, we’re headed to 100,000 in 2-3 weeks without change.”

As debates rage about how the crisis should be handling on both the health and economic fronts, The Conversation has learned the Prime Minister’s office heard sharply conflicting views from two economists at a dinner in Parliament House’s private dining room on Tuesday March 17.

The economists were Henry Ergas, who previously worked at the OECD and has advised companies and governments, and Warwick McKibbin, professor of public policy at the Australian National University. Present were Scott Morrison’s chief of staff John Kunkel and senior bureaucrats.

The view Ergas presented was substantially the same as he wrote in the Australian on Friday when he warned of the dangers of going “too far” in the efforts to combat the spread of the virus.

He wrote: “Whatever governments do should preserve, to the greatest extent possible, the economy’s ability to rebound, including by limiting the debt that is loaded on to companies and individuals.

“Would such an approach save as many lives as a complete shutdown? Possibly not. However, if it could achieve two-thirds of the health objectives at one-third the costs, it would be reckless not to choose it”.

McKibbin argued the line of epidemiologists that it was best to try to stop the spread as fast and comprehensively as possible, with drastic measures.

He proposed companies and individuals should be supported with a system of contingent loans – like the student loan scheme – that would be paid back later via the tax system but only when the firm or individual passed, respectively, a certain cash flow or income level.

Morrison has repeatedly given equivalence to the health crisis and the economic crisis. The government will release within days its third package of economic support which will aim to put businesses into “hibernation” so they can restart later. It is expected to include some form of wage subsidy.

On Sunday Morrison appealed to employers to wait to see the package before doing anything.

“I would say to employers, who I know are going through very difficult times, these changes will be announced soon and I would ask that before you make any further decisions that you take the opportunity to see the further measures.”

Morrison said the next package would be “bigger than anything you have so far seen”. The last package was $66 billion.

It would “ensure that we are working together with companies to keep people connected to companies”.

The package would include support for those who had recently been the victims of closures.

In an open letter released on Sunday more than 100 Australians including economic, social and public policy experts, unionists, consultants, writers, business people and religious leaders, called for “a Liveable Income Guarantee” to protect people.

For further information on the coronavirus, considering downloading the government’s coronavirus app available on Apple and Android.The Conversation

Michelle Grattan, Professorial Fellow, University of Canberra

This article is republished from The Conversation under a Creative Commons license. Read the original article.

How to flatten the curve of coronavirus, a mathematician explains



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Andrew Black, University of Adelaide; Dennis Liu, University of Adelaide, and Lewis Mitchell, University of Adelaide

People travelling into Australia will now have to self-isolate for 14 days – one of a range of measures announced at the weekend by Prime Minister Scott Morrison, with the aim of slowing the spread of the coronavirus and easing the stress on hospital beds.

This general concept of slowing the virus’s spread has been termed “flattening the curve” by epidemiologists – experts who study how often diseases occur in different populations, and why. The term has become widespread on social media as the public is encouraged to practise “social distancing”.

But how does social distancing help to flatten the curve? We can explain by referring to what mathematicians call “exponential growth”.

Exponential growth

In the early stages of an epidemic, when most people are susceptible to infection, mathematicians can model a disease’s spread from person to person as essentially a random “branching process”.

This diagram shows the number of cases, over time, in a branching process with exponential growth. Author Provided.

If one infected person infects two others on average, the number of infected people doubles each generation. This compounding is known as exponential growth.

Of course, an infected person is not definitely going to infect others. There are many factors affecting the likelihood of infection. In a pandemic, the growth rate depends on the average number of people one person can infect, and the time it takes for those people to become infectious themselves.




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Research suggests the number of confirmed COVID-19 cases is growing exponentially worldwide with the number doubling about every six days

Exponential growth models closely match reality when starting with a small number of infected individuals in a large population, such as when the virus first emerged in Wuhan, or when it arrived in Italy or Iran.

But it’s not a good model once a large number of people have been infected. This is because the chance of an infected person contacting a susceptible person declines, simply because there are fewer susceptible people around, and a growing fraction of people have recovered and developed some level of immunity.

Eventually, the chances of an infected person contacting a susceptible person becomes low enough that the rate of infection decreases, leading to fewer cases and eventually, the end of the viral spread.

Flatten the curve

Health authorities around the world have been unable to completely prevent COVID-19’s spread. If cases double every six days, then hospitals, and intensive care units (ICUs) in particular, will be quickly overwhelmed, leaving patients without the necessary care.

But the growth rate can be slowed by reducing the average number of cases that a single case gives rise to.

In doing so, the same number of people will probably be infected, and the epidemic will last longer, but the number of severe cases will be spread out. This means that if you plot a graph of the number of cases over time, the rising and falling curve is longer but its peak is lower. By “flattening the curve” in this way, ICUs will be less likely to run out of capacity.

Flattening the curve is another way of saying slowing the spread. The epidemic is lengthened, but we reduce the number of severe cases, causing less burden on public health systems. The Conversation/CC BY ND

As there is currently no vaccine or specific drug for COVID-19, the only ways we can reduce transmission is through good hygiene, isolating suspected cases, and by social distancing measures such as cancelling large events and closing schools.

Avoid “super-spreaders”

Of course, the situation is not quite as straightforward as a simple branching process. Some people interact more than others, and might come into contact with many different groups.




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Mathematicians model these connections as a social network, such as the one below. Infected people are red nodes, and susceptible people are blue. The large node in the middle of the diagram is a super-spreader, a person who connects with many others, and thus has more potential to spread the disease.

This graph shows how an epidemic might spread across a network over time. Blue dots are susceptible individuals, while red dots are infected people. Two dots are connected by a line if they are in contact with each other, and the more contacts a person has, the bigger their dot is on the network. Author provided

Interventions help remove nodes and break connections.

In the diagram above, the large, highly connected central node would be the best one to remove to break connections. This is why it’s a good idea to avoid large public gatherings during the COVID-19 outbreak.

Mathematical simulations of social distancing have shown how breaking the network apart helps flatten the curve of infection.

How maths is helping

How much social distancing is required to flatten the curve enough to stop hospitals being overwhelmed? Is it enough to quarantine people who have been in contact with confirmed cases? Do we need widespread closure of events, schools and workplaces?

Answers to these questions require mathematical modelling.

We are still in the early stages of the COVID-19 outbreak and there is great uncertainty about the characteristics of this virus. To accurately forecast COVID-19’s growth, the underlying dynamics of transmission need to be determined.

These are driven by factors including:

  • How many people on average does an individual infect? (the “reproduction number” which, according to the World Health Organisation, is currently between 1.4–2.5 people)
  • How long until the onset of symptoms? (the “incubation period”, which is estimated to be 5.1 days)
  • What proportion of transmission occurs prior to the onset of symptoms, if any?

As such data is collected and integrated into models over the coming months, we will be better placed to offer accurate predictions about the course of COVID-19.

Until then, it’s better to err on the side of caution and take swift action to slow transmission, rather than risk a spike in cases, and put strain on our health system.The Conversation

Andrew Black, Lecturer in Applied Mathematics, University of Adelaide; Dennis Liu, PhD Candidate, University of Adelaide, and Lewis Mitchell, Senior Lecturer in Applied Mathematics, University of Adelaide

This article is republished from The Conversation under a Creative Commons license. Read the original article.