Covid-19: Where do we stand now?

While the world is grappling with the deadly coronavirus, there’s a lot of discussion on the “curve” representing the projected number of people who will contract COVID-19 over a period of time. This bell-shaped curve is not about the true numbers, but only predictions. Depending on the infection rate, the curve might be steep, in which the virus spreads at a rapid rate, with the number of cases reaching its peak quickly. It usually experiences a steep fall thereafter.

There has been a widespread call for “flattening the curve”. As we are seeing in Italy, rapid growth rate of the epidemic makes the hospital and basic medical facilities exhausted in no time, leaving  scores of patients untreated. Flattening the curve thus slows the spread of the epidemic, and pulls the curve down — quite often by implementing “social distancing” aggressively.

A flatter curve will have the same number of people infected, but over a longer period. A slower infection rate would result in fewer patients being deprived of basic treatment. This gives the hospitals, health personnel, police, administration, and scientists engaged in finding vaccines more time to prepare and respond to the crisis. Spreading out the tidal wave of cases would certainly save many lives. Thus, understanding and managing the surge of the curve, and to pull it down successfully is an important part of the battle against an epidemic.

 A classic example of its effectiveness can be traced in the history of the century-old Spanish flu pandemic (1918), which infected 500 million people worldwide. The US city of Philadelphia ignored the warnings of  experts, and about 16,000 died in the city in six months. In contrast, another US city, St. Louis, could successfully flatten the curve by quickly implementing social isolation strategies, and it experienced 2,000 deaths.

An important indicator of an epidemic is the reproduction number (R), which indicates how many people an infected person further sickens on an average. If R is above 1, infections grow exponentially into an epidemic. If it’s below 1, they die down. And hence the idea is to reduce R as much as possible. A fancy term, “The Hammer and the Dance”, has been popularised by Silicon Valley marketing-leader Tomas Pueyo. Pueyo argued that strong measures like “hammer” should be adopted initially to take “R as close to zero, as fast as possible, to quench the epidemic.” In Wuhan, R went down to 0.32 from 3.9 due to the lockdown. The dance stage, subsequently, resembles small ripples, and Pueyo argued that “once you move into the dance, you ...just need your R to stay below 1”.

Let’s look at the case data of Covid-19 in different countries. The curve of cumulative number of cases resembles a prolonged “S”. The increments per day are small initially, and it grows rapidly thereafter. The trajectory of the curve determines how the numbers grow. The “rate of increase” is the daily new cases. The epidemic maintains a bull-run as long as the number of new cases in a day minus the number of new cases the previous day remains grossly positive. When this changes sign, that’s an inflexion point, and usually that should roughly correspond to the mid-point of the epidemic. The cumulative curve will increase thereafter at a slower rate, and it will eventually become horizontal. In real life, however, the curves may not be so well-behaved.

China has now reportedly controlled its Covid-19 epidemic. A study on the daily data from January 22 to March 22 shows that South Korea, mostly due to its aggressive social-distancing and testing, too has shown remarkable success in controlling the virus. South Korea reached the inflexion point of the epidemic on March 3-4, with nearly 5,500 total cases. Korea is now at the end-phase of this epidemic with a total number of 8,897 cases as of March 22. And the country may eventually be able to restrict the epidemic within another 2,500-3,000 cases. Japan, with 1,086 cases as of March 22, seems to have almost reached near the inflexion point, unless it loses its grip over the situation. The curve for Singapore, however, showed a mild sign of inflexion around February 19, with only 84 cases, but has surged since March 5, rising sharply during the last few days, and it’s nowhere close to the mid-point yet. The sorry state of Italy continues with nearly 60,000 cases so far, as its curve is sharply increasing with no sign of inflexion point anytime soon. The cumulative curves for Spain, France, and the US are also steeply increasing at the moment with no clarity on inflexion points.

India’s situation, like that of Russia at the moment, is similar — we haven’t missed the bus yet, for sure; but we’re nowhere close to the inflexion point yet. Although many experts have predicted a different eventual number of cases for India assuming different kinds of models, I think that the correct model for India is impossible to predict — for the simple reason that we’re in the early stage of the curve, and we don’t have enough data yet to estimate the future. The slope of the curve is quite steep during the last six days or so. Hopefully, aggressive social distancing by imposing curfew and lockdown in different parts of the country will help, and we’ll be able to see the mid-point soon.

The writer is a professor of statistics at the Indian Statistical Institute, Kolkata