You can't see the virus behind the world's latest pandemic with the naked eye but, plotted on a graph, it looks like one side of a mountain, climbing skyward as cases of COVID-19 soar past half a million worldwide. Eventually, epidemiologists say, that trajectory will start to fall. Immunity in the population will build up against the mystery illness and it will begin to taper off.

But in the middle, there will still be that mountain peak – the "curve" everyone is talking about. The steeper it is, the more exponential the spread of the virus; the flatter it is, the slower, the less stress on health services and the more lives that will be saved in the months ahead without a vaccine.

So how do we flatten the curve? What is herd immunity? And what are countries around the world, including Australia, doing to fix the picture?

What do we mean by 'flattening the curve'?

The fight against COVID-19 is about medicine, of course. But it’s also about mathematics (and money). When a new epidemic explodes onto the scene, experts look for two main numbers: how many people each patient will infect and how many people will die from the disease. This helps them plot an arc for the outbreak: how far it will likely spread before a vaccine is rolled out or enough people who have recovered from the illness with virus-fighting antibodies in their system build up "herd immunity" against it.

Flattening this curve means slowing how fast the virus moves through the community. And it needs us to move. So limiting opportunities for the bug to jump from person to person – by adopting "social distancing" measures such as staying 1.5 metres away from others and avoiding public spaces as well as improving hygiene and isolating those infected or exposed – will stretch out the spread of COVID-19 over time, giving doctors, economies (and vaccine-makers) space to breathe.

When the curve keeps climbing, countries see a surge of cases needing medical intervention all at once and hospitals can even run out of life-saving machines such as ventilators or protective gear for frontline staff. That pushes up the death toll and forces impossible triage choices such as the ones that have already faced doctors on the frontlines of the northern Italian outbreak (where it was suggested older patients should be turned away to leave beds for younger patients in their 40s and 50s). It's why some doctors, including in Australia, say simply flattening the curve is not enough to push it back within the reach of the healthcare system – the virus must be stopped in its tracks through containment in line with what the World Health Organisation is calling for, and even the lockdowns seen in China and New Zealand.

How is the maths looking for this pandemic?

So far it's estimated about one in five people infected with the new virus will need medical intervention such as oxygen or ventilation to recover and about 1 per cent of all patients will die. That's 10 times higher than the mortality rate for seasonal flu but still much less than the first (and now infamous) coronavirus outbreak SARS in 2003. Unfortunately, the new virus is also more infectious. Each person with COVID-19 is likely to infect two or three people – meaning that growth curve can quickly become exponential, according to the Grattan Institute.

Every day counts once the pandemic clock starts ticking, warns Dr Michael Ryan, who heads up the WHO's emergency response team. "Be fast. Have no regrets," he told the world on March 13. "You must be the first mover. The virus will always get you if you don’t move quickly."

During the world's last severe pandemic, the 1918 Spanish flu, the US city of Philadelphia took 14 days to mount a public health response after its first case, even pressing ahead with a big public march. St Louis, meanwhile, cracked down on people's movement and gatherings within just two days of the influenza strain entering its borders. By the end of the crisis, its death toll was less than half of Philadelphia's.

How are countries coping with the coronavirus?

Dr Stephen Duckett and his colleagues at Grattan have been tracking the scale and speed of new COVID-19 infections in nations all around the world. Cases might appear in just a trickle at first but, once countries crack the 100 mark, the virus seems to either explode rapidly – such as in China, initially, and then Iran, Italy, the US, and Spain – or slow to a flatter line as has been recorded in places such as Singapore and Hong Kong.

Dr Duckett says nations that moved fast to test and track suspected cases and then brought in tough social distancing or containment measures along the lines of the St Louis model have already seen their infection growth fall, even after rapid early spread. In lieu of a vaccine, many countries – and some Australian states – are also closing borders, raising barricades and shutting down much of daily life.

In Australia, tough new social distancing measures seem to be working. The daily growth in new infections has already fallen from about 30 per cent in mid-March to less than 2 per cent in April. But if people do not follow the rules, Chief Medical Officer Brendan Murphy warns we could lose our window to contain (and even eliminate) the outbreak – and cases could rapidly explode again. Meanwhile, other countries which flattened the curve early on, such as China and Singapore, have already softened restrictions. China so far has not seen cases shoot back up, under a dreaded "second wave" of infections but in Singapore a sharp rise in cases has since forced the government to step up restrictions, closing schools and most workplaces until May 4.

Do lockdowns work? What can China teach us?

COVID-19 first emerged in humans in late 2019, at a wet market in the sprawling city of Wuhan, China. The illness was not formally linked to a new strain of coronavirus until early January, when millions of people were already travelling for the country's biggest holiday, Lunar New Year. Infections exploded.

But then China's Communist government did something without precedent in modern times – it locked down cities and transport across huge swathes of the country, grounding tens of millions. Factories shut down. Schools and offices closed. Streets emptied.

At the time, such a move seemed unthinkable in a Western democracy. But, in the maths, it appears to be working. China was clocking up more than 3000 new cases a day in early February. By mid-March, that number had fallen to less than 30 and on March 19 it recorded none at all for the first time, apart from those imported from other countries. Its government has already claimed "a great victory" over the virus and has started to wind back lockdowns even as other nations such as the US raise doubts about its official infections tallies. The WHO says the turnaround is a sign the pandemic can still be contained with "aggressive measures", lashing countries for their slow responses thus far.

It's still unclear if or how fast lockdowns will work for Europe and the US - the next frontiers of the pandemic. In Italy and Iran, early cases appeared to again spread under the radar until a sudden surge hit hospitals (and even Iran's parliament). Both governments were fairly slow to act; in Iran, for reportedly political reasons.

In Italy, the government was reluctant to impose draconian measures on its densely populated cities. Should it really turn away soccer fans from matches? Or close bars and order people back into their homes from piazzas? But the blockades in the north, where the outbreak began, failed to stop infections leaking into the rest of the country and beyond. Italy has since gone into its own style of lockdown, followed by countries such as Spain, France, German, New Zealand, the UK and some US cities.

In some countries, including Australia, the virus's reproduction number - or the likely number of people each person will infect - has already fallen from its natural average of 2 to 3. If it keeps falling, to below one, the virus will start to die out on its own. Australia's deputy Chief Medical Officer Professor Paul Kelly says the nation is on the cusp of killing off the virus but the government has flagged pursuing full elimination of the virus (along the lines of the tough lockdowns seen in New Zealand) would be too costly.

What other measures have worked?

Some experts point out that the two countries that appear to have turned the tide on a rapid outbreak – China and South Korea – have gone further than just lockdowns. Knowing that most infections so far have come from close contact in hospitals or family groups, China and South Korea take those who test positive out of their homes into dedicated health centres for isolation. The move is recommended by the WHO and also done in places like Singapore but has raised serious human right rights concerns in China. Horror stories of infection circulating in SARS quarantine still cast a long shadow in China but this time milder cases are kept together in huge pop-up fever clinics, often in converted stadiums and gymnasiums, and those still being tested reportedly kept away from confirmed cases.

Both China and South Korea, including early success stories such as Singapore, Hong Kong and Taiwan, have also been aggressively hunting for cases – temperatures are taken before entering any building. If you have a fever, you must roll up to a specialised clinic or "drive-through" for testing.

These parts of the world have been hit hard by dangerous coronavirus outbreaks of the past, including SARS, Dr Duckett notes, and so their people were already primed for the health checks to come. When word came from China that another coronavirus had jumped from animals to humans, countries such as Singapore and Taiwan acted quickly. In some jurisidictions, social distancing has played out without need for stricter lockdowns or domestic travel bans. While Hong Kong faced criticism for not closing its borders to mainland China fast enough, months of anti-Beijing protests meant schools were already teaching online and many people working from home.

South Korea, meanwhile, saw the virus erupt within a religious sect and quickly deployed particularly exhaustive detective work to track close contacts of known cases – famously using CCTV to trace people back to a specific bus or taxi.

The island nation of Singapore looked in danger of being overrun in February when it was recording the second-highest volume of cases outside China. It flattened its curve through quick detection and diagnosis as well as strictly enforced home quarantines (featuring spot checks and twice-daily location monitoring with serious penalties applying for a breach.) As cases crept up again in March, the government hit the brakes. "We have decided that instead of tightening incrementally over the next few weeks, we should make a decisive move now, to pre-empt escalating infections," said Prime Minister Lee Hsien Loong.

The use of technology has proven both useful and potentially troubling. Countries such as China, Iran and Israel are deploying their notoriously invasive surveillance networks, including tracking phones, to keep tabs on people under isolation and close in on suspected cases. Australia also has powers to order people into quarantine and states have mobilised police forces and even the Australian army to help enforce such orders.

Dr Dunckett notes that in China and South Korea, growth in cases might be down but overall new infections still linger between between 200 and 600 a week, showing that "getting to near-zero new cases is not a given" even once countries slow the spread.

How important is testing?

WHO director-general Tedros Adhanom Ghebreyesus has blasted governments around the world for giving up on widespread testing and contact tracing, "the backbone" of any response, even as they ramp up social distancing measures.

"You cannot fight a fire blindfolded and we cannot stop this pandemic if we don't know who is infected," he said on March 16. "Test every suspected case. If they test positive, isolate them and find out who they have been in contact with. And test those people too."

A lab test for samples of the virus was created quickly but swabs and reagents needed to study the virus's DNA in a lab are running low worldwide. Faster blood tests are still only widely available in China. And both methods can be fooled if the virus is missed in a sample from a throat or nose swab or antibodies against it are not yet present in a patients blood.

In China, diagnosis has been industrialised. At a fever clinic, you will be met by a healthcare worker in full protective gear, testing white blood cell counts and deploying portable scanners to check for the tell-tale "ground glass" inflammation of COVID-19 in the lungs. Even there, a recent study found two-thirds of reported cases could be traced back to undiagnosed patients – suggesting the virus could be spreading under the radar even from people with fewer symptoms who shed less virus.

In the US, low testing rates and diagnosis delays from a botched roll-out of initial tests have been blamed for a disastrous explosion of cases that saw America become ground zero for the virus, recording more than half a million cases by early April. Extending the timeline for social distancing measures, President Donald Trump said if the US could hold down the death count to 100,000 it would show the country had done a "very good job".

Australia's testing rates are proportionately high compared to many other countries around the world (about 300,000 have been done so far) but the criteria for being tested is still fairly strict, as testing kits run low. In recent weeks, more states have been relaxing the rules and even beginning random sample testing of people with symptoms but none of the usual risk factors for a swab: overseas travel or contact with a confirmed case. Professor Murphy notes Australia has one of the lowest positive rates for testing in the world (about 2 per cent), meaning authorities feel "reasonably confident that we are detecting a significant majority of cases in Australia and that means we can get on top of cases" through contact tracing. That's in contrast to countries such as Iran, Italy and the US, where Australian authorities say they likely only tested the more severe cases or, as Murphy puts it, "when they detected significant outbreaks they probably had much, much larger outbreaks in community that were undetected".

At times, Australian health authorities have also faced criticism for letting cases slip through the net, most notably allowing 2700 passengers to disembark in Sydney from the Ruby Princess cruise ship, 400 of whom later tested positive.

What is herd immunity?

The term "herd immunity" went viral in March amid speculation that Britain's government was lagging behind other nations in imposing social distancing measures as part of a bold plan to allow the virus to sweep through the population, (and so build up their immunity against it). 

In the modern era, community resistance to a virus is commonly achieved through a vaccine. Experts, including in Australia, have warned that stalling protections against COVID-19 for the sake of encouraging natural resistance among "the herd" could be "catastrophic", costing lives without much slowdown. That's because it's still unclear how well and for how long people are immune to the virus once they recover. It's also still unclear if COVID-19 will burn out entirely as recoveries rise and the seasons change or if it will linger or even mutate and return into the population at a later stage.

The United Kingdom had planned to seal off its most vulnerable, such as the old and unwell, and delay other protections, thereby allowing the virus to sweep through the general population quickly. But following stern advice from experts, its since brought forward a full-scale shutdown, closing schools and telling people to stay home from work.

The Netherlands has since revealed it will embrace a COVID-19 strategy of its own based on herd immunity, saying mass lockdowns are not feasible.

Part of the challenge facing world leaders is balancing the threat of the virus against the huge disruption of containment, which experts warn could bring its own health costs. Analysis of virus-fighting strategies by the Imperial College London found more targeted measures such as isolating those exposed to the virus or at risk of serious complications could reduce peak demand on hospitals by about two thirds. But this would still result in hundreds of thousands of deaths in the UK alone. Instead researchers recommended a wider, though more difficult "suppression", where people across the community stay home more often and distance themselves from each other until a vaccine can be rolled out.

The problem, as Professor Murphy in Australia has also stressed, is keeping it up over the months ahead without burnout. "You can't just shut things down for two weeks and that's it. It has to keep going."

This article was originally published on March 18 but has been updated to reflect new developments both worldwide and in Australia.