The number of Covid-19 cases worldwide has passed the one million mark. Tens of thousands have died. Many countries are in lockdown mode and face a recession.

Last Friday, the Singapore Government announced strict social distancing rules that will kick in from today. These include closing all businesses, except those offering essential services, and schools.

These measures are necessary as Singapore now has over 1,300 cases. Dozens of new local cases arise every day, a significant number of them unlinked. There are clusters in foreign worker dormitories and cases among healthcare workers.

As late as early February, some people were still saying that the coronavirus outbreak was like a bad case of flu and decrying the border closures and quarantine measures taken.

Today, it is clear, from how Covid-19 ravages Europe and America, that the outbreak can spiral quickly out of control if societies continue with business as usual.

Singapore's efforts, from a medical or healthcare perspective, to battle the scourge of Covid-19 can be summarised in two points.

First, at the public health and community level: to keep effective the reproductive ratio of the virus at less than 1.

Second, at the clinical and hospital level: to keep fatalities down by not allowing our hospital services, especially intensive care unit services, to be overwhelmed.

DISEASE DYNAMICS

Communicable disease outbreak control is always a race against time. Time wasted or chances missed means many more cases and lives lost to the disease.

The measures imposed from today buy the country a valuable four weeks in which to get the reproductive ratio down and break the transmission cycle.

Reproductive ratio, or R0, is the number of additional cases each case is expected to generate in the course of the case being infectious.

The basic R0 is the reproductive ratio of a disease in the absence of any deliberate intervention in disease transmission, or in its "natural" state, where societies do not practise interventions like social distancing or lockdowns and everyone is susceptible to the disease.

The World Health Organisation website has estimated the basic R0 of Covid-19 to be between 2 and 2.5.

On the other hand, the effective reproductive ratio (R or Rt) is the prevailing reproductive ratio after interventions such as social distancing have been put in place.

The aim of every country now is to bring their Rt from its "natural" state or R0 of 2 to 2.5, to below 1 through various interventions.

When Rt is less than 1, the size of the infected pool of people shrinks with time. The pool increases in size if Rt exceeds 1 - that is, there will be a growing epidemic.

TIME MATTERS

The dimension of time in controlling epidemics and pandemics cannot be overemphasised.

Doubling time is the time taken for the infection numbers to double.

Incubation period is the period from infection to developing symptoms. In a paper published by Singapore researchers in The Lancet on March 28, the median incubation period for Covid-19 was four days.

Another time-based measure to note is serial interval - the time between successive cases in a chain of transmission. In a recent paper published in the journal Emerging Infectious Diseases based on Chinese data outside of Hubei province, the mean serial interval time was estimated to be four days.

Since the median incubation period and mean serial interval time are both about four days, this would imply that there is significant asymptomatic or pre-symptomatic transmission.

This is a very important epidemiological feature of Covid-19 that makes it different from Sars (severe acute respiratory syndrome) and also more dangerous.

CUTTING DOWN RT

The fastest and most effective way to cut down on Rt - the effective reproductive ratio - quickly is to practise social distancing.

If a case has close contact with half the usual number of persons in a normal day for the entire period he is infectious, his Rt is half of the basic R0.

The Rt for an entire community is likewise halved if everyone practises social distancing and halves his number of close contacts over time.

For example, if on average a person meets 50 people a day in his usual daily routine, and through social distancing he meets only 25 people, then if he gets infected, he will infect half the number of people had he not practised social distancing. Once halved, the overall cluster numbers become a lot more manageable.

Let's take an example from the table. Assume that serial interval is four, and Rt is 2.5. That is, each case gets transmitted to 2.5 other cases over a cycle of four days each.

At this rate, in 16 days there will be 64 cases. In 28 days, there will be a whopping 1,016 cases.

Now assume that social distancing measures kick in, and we manage to bring the Rt to 1.25. Assuming the same serial interval of four, in 16 days there will be eight cases and after 28 days, there will be only 19. These are much smaller than when Rt was 2.5.

Once numbers are brought under control, a good field epidemiology team can investigate an outbreak and quarantine close contacts in about two weeks.

Besides social distancing, good personal hygiene, such as frequent hand washing and not touching one's face as well as appropriate mask-wearing, also helps to bring down the Rt significantly.

Serial interval also has a dramatic effect on the cluster size. Shortening the serial interval by just one day will increase the cluster size by multiples.

A cluster needs to be aggressively contained within two weeks of the first case because by the time one month has passed, the size of the problem has mushroomed to probably crisis levels.

Unfortunately, while we can change our behaviour to cut down the Rt quickly, serial interval is a characteristic of the virus that is not easily altered; hence, quick and decisive action to contain a cluster, such as via contact tracing and quarantine, is most important.

Understanding the basics of epidemiology helps us appreciate the need to cut down the reproductive ratio and the need to act very quickly.

Left uncontained, a single case can lead to a cluster of about 100 to 200 plus cases in about a month if the serial interval is between four and five days and the R0 is 2.

If the R0 is 2.5, then the cluster size becomes calamitous: A single case may have spawned 400 to 1,000 cases. This may have been what has happened in places such as Italy, Spain, the United States or the United Kingdom.

Singapore has been aggressively contact tracing every case and ring-fencing them, to reduce the Rt.

We need to step up our control measures. Unlike the earlier rounds, which depended more on government and healthcare workers, this round of measures requires all our compliance and discipline.

Each of us can play an important role in this race against time to bring down our infection numbers. We must do it or face the consequences.

• Wong Chiang Yin is a public health specialist and the group CEO of a private hospital group in Singapore. He was president of the Singapore Medical Association (2006 to 2009) and is the scribe of the Academy of Medicine of Singapore.