Taking a look at other global pandemic death tolls like the Bubonic plague might make you feel a bit better about the current situation.

Australia’s chief medical officer, Professor Brendan Murphy, says the true number of coronavirus cases around the world may be five or even ten times higher than the current official estimate.

“Worldwide, we’ve now passed a million reported cases of COVID-19,” Prof Murphy said at a press conference with Prime Minister Scott Morrison in Canberra this afternoon.

“We believe that the true number is probably five or ten times as much as that, because we know that judging by the death rate, the testing rate, in many countries they’re not detecting all the cases. There are some countries that don’t have the capacity to test.”

The official tally reached one million people today. According to Johns Hopkins University, there are now 1,015,709 confirmed cases of the coronavirus around the world, with 53,030 deaths.

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The United States has the highest number of reported cases with 245,213. Italy and Spain have each passed 100,000 as well.

“In Australia, we’re now reporting 5274 cases,” Prof Murphy said.

“But in Australia we’re pretty confident that our testing has been probably the best in the world. We are very confident that while there will certainly be some undetected cases, we have a pretty good idea of the size of our outbreak.”

He said the government’s medical advice panel was “quietly pleased” with Australia’s direction, but “we cannot stop” imposing measures to keep the virus under control, as community transmissions were still occurring.

Later in the media conference, Prof Murphy was asked whether he believed the official figures coming out of China - a particularly contentious issue at the moment.

Yesterday Bloomberg News revealed the existence of a classified US intelligence report, which concluded China was giving an inaccurate number of cases and deaths to the rest of the world. China has since responded angrily to the accusation.

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“I think the only numbers I have total faith in are the Australian numbers, frankly, because we have the highest testing rate in the world,” Prof Murphy said.

“I think China is in a really difficult position. They did clamp down incredibly hard, and they stopped transmission. But their population is not immune. They still have a lot of people in their population and they are, obviously, trying very hard to prevent a second wave.

“I think they have been pretty transparent, but as I said, I’m only confident about our numbers. I’m certainly not confident even the numbers out of the US aren’t much higher than are being reported, because nobody else in the world has been doing testing like we have.

“Nobody else in the world got on to all those original cases out of Wuhan in January and contained them. That’s why we are now dealing with what we know, rather than a huge community transmission that happened all through February in countries like Italy and the US. We’re on top of the cases. But we still have a long way to go.”

Mr Morrison was also full of praise for Australia’s response to the pandemic. He shared estimates of where the country would be if it had not adopted tougher social distancing measures in the last fortnight.

“Had the virus kept growing at the same rate it was 12 days ago, we would now have more than 10,500 cases,” the Prime Minister said.

“This is a tribute to the work being done by Australians in getting around and supporting the measures being put all around the country.”

He said Australia was now at “single digit rates of growth” in the number of cases, but added that more still needed to be done.

“We are in what we described today in National Cabinet as the ‘suppression phase’. We are now in a place where we are seeking to put the pressure down on constraining this virus in Australia,” said Mr Morrison.

“We then need to look at the recovery phase, which is beyond. And I want to assure Australians that the National Cabinet is very focused on those issues as well.

“But in these early phases, the work has had to necessarily focus on establishing all the rules, establishing the restrictions, putting the economic supports in place.”

The government has been under pressure to release the modelling underpinning its coronavirus response. On Monday, deputy chief medical officer Paul Kelly implied that would happen this week, but he later walked back that promise.

This afternoon Mr Morrison told Australians to expect the modelling next week.

“Today we had a further report on modelling work that had been done. That modelling work is not yet complete. That modelling work looks at different scenarios so we can be confident to an acceptable level that the potential course of the virus in Australia will run at a pace in which our health systems will be able to support the Australian population,” he said.

“The early news on some of this early modelling is that at the current rate, if we keep doing what we’re doing, and we keep doing the work to upgrade our ICU capacity and secure the extra ventilators and all the things we are doing right now, then right now that trajectory is promising. It is encouraging.

“But there are no guarantees, I want to express. This virus writes its own rules. We have to seek to try and understand them as best we can and respond as best we can to the pressures that we face.”

He said “further work” would be done on the modelling in the coming days and it will be reviewed again when the National Cabinet meets on Tuesday morning. That will be followed by a briefing, at which the information will be shared publicly.