These are desperate times in the national capital. ICUs are full and there are critical shortages of medical oxygen. Almost every ventilator bed in the city is occupied. Tuesday saw 277 Covid-19 deaths, a number far higher than ever before – leaving aside a “reconciliation” in June last year when old fatalities were added into the count.

The city has averaged around 23,000 positive cases a day over the past week. This is almost three times higher than ever seen in 2020. Moreover, about a quarter of tests have come back positive in the past week, indicating that an increasing fraction of infections are going unrecorded.

Delhi’s epidemic so far

What makes this unfolding story all the more remarkable is that this is Delhi’s fourth Covid-19 surge. The first peak in cases was in late June 2020. Cases subsided and then surged again, peaking in September, falling a little, and then climbing again to another high in November. Then began a clear and steady improvement.

By the middle of February 2021, there were around 1,000 cases and 10-15 deaths occurring a week. To see the scale of this improvement compare these figures with previous highs of over 50,000 cases and 800 deaths a week. This huge calming of the epidemic occurred even as the city opened up and life went back to some kind of normality.

It would have seemed reasonable for city dwellers to feel the worst was over. What they did not know was that this was the calm before a huge storm.

Cases started to creep up in mid-February. The process was so slow that at first it was hard to spot in the data. A month later, by mid-March, the city was seeing around 500 daily cases. In a city of close to 20 million and with around 70,000 tests being done daily, this did not yet appear an alarming number of cases.

Then there was a huge acceleration. We can measure the speed at which an epidemic is growing by estimating “R”, its “effective reproduction number”. This number tells us, approximately, how many people one infected person is infecting. Estimating R is a little tricky, but the key observation is: if R is above 1, then the epidemic is growing; if R is below 1 then it is subsiding.

In the latter half of March, R crossed 1.5, and for much of April, R has been around 2, which corresponds to cases doubling roughly every five days. This very rapid growth shows up in the graphs as a near vertical ascent. With such a steep rise, weekly cases broke all previous records around April 12. But they continued to rise, and are now at three times 2020 record values.

R has fallen a little in the last few days, but this gives little cause for hope. The fall may partly reflect testing falling behind the sharp rise in infections. Test positivity has shot up, rising from 2% to over 25% in the last three weeks – a strong sign that a larger and larger fraction of infections just aren’t being captured in testing.

Why is the rapid surge so shocking?

In January 2021, a seroprevalence survey (or “serosurvey” for short), found antibodies to SARS-CoV-2, the virus which causes Covid-19, in about 56% of Delhi’s population. The conclusion is that around 56% of city-dwellers had been infected by the virus at some point during 2020 – possibly more, as not every prior infection necessarily shows up in an antibody test.

The estimate of 56% previously infected tallies well with earlier calculations based on the city’s four serosurveys in 2020, alongside case and fatality data. Taking all the data together we can be quite confident that more than half of the city had been infected by SARS-CoV-2 during 2020.

This point is worth emphasising because some commentators looking in horror at Covid-19 surging in Indian cities have questioned whether these cities really could have seen such high previous infection. In Delhi’s case there is a lot of data pointing this way.

A cautious assessment in January would have been: the city is still vulnerable to a resurgence, but it should be limited in speed and total size because so many have already been infected. Instead, the city is seeing a tsunami of new infections.

Exactly how many new infections are occurring every week? To answer this requires estimating how many infections are being detected and appearing in the daily case counts. Case and serosurvey data suggests that around 6% of infections were detected during 2020. But this average figure actually hides very poor early detection and a big improvement later in the year, when detection was likely around 10%.

If we are optimistic and assume that 10% of infections are being detected today, then last week’s 1.6 lakh cases would reflect an astonishing 1.6 million infections. If so, then in one week, over 8% of the city was infected. And that is a very conservative estimate – the reality could well be higher.

It is not just this scale – the sheer number of infections – which is remarkable. It is also the speed with which infection has spread, captured by R hovering near 2. To see why this is surprising we need a little theory.

In the very early days of an epidemic, prior to many infections or restrictions, R is termed “R0”, or the “basic reproduction number”. R0 should be the maximum possible value of R. If you have measures to slow the spread – masking, people avoiding gatherings, and so forth – this brings R below R0. And if you have a significant number of people immune to the disease because they have been infected or vaccinated, this should bring R down further still.

For example, if half of a population becomes immune to a disease, this should halve R. My estimate of R0 using Delhi’s very early data is 2.8. With half the city infected, the maths implies that R just should not be anywhere close to 2.

Why is mortality higher in Delhi?

Before trying to resolve this conundrum, let’s compare Delhi’s and Mumbai’s epidemics. Mumbai too is witnessing a devastating surge which is proving very hard to control. The similarities and differences could be important.

Both cities saw several waves of infection in 2020. Infection spread faster in Mumbai in the early days, but Delhi gradually caught up. By the end of the year, around 60% in Mumbai had been infected, close to the value of 56% estimated for Delhi.

Mumbai’s data had a strong asymmetry: slum-dwellers were much more likely to have been infected than residents of building societies. This meant that the city’s more middle-class areas remained more vulnerable to new infection. It is possible that a similar asymmetry existed in Delhi, although the data to confirm this is more limited.

Mumbai’s epidemic stabilised, but the city never saw Delhi’s convincing wind-down by early 2021. If we look at cases and recorded deaths per capita, Delhi’s lowest numbers were about 80% lower than Mumbai’s. Mumbai’s epidemic chugged along, while Delhi’s almost came to a halt.

Perhaps for this reason the latest wave became apparent in Mumbai earlier than in Delhi. A rise in cases began in February, and already by mid-March Mumbai’s weekly cases had broken all previous records. They went on to quadruple by early April, before starting a very slow and halting decline around April 10.

By contrast, Delhi’s cases only crashed through previous records in the second week of April – and they are still shooting up.

R in Mumbai never reached the dizzying heights seen in Delhi – but it got quite close, touching about 1.7 in late March before decreasing. As in Delhi, test positivity rose to a peak of over 20%.

Apart from timing, most aspects of the two cities’ current surges seem similar. But there is one rather striking difference. Recorded Covid-19 deaths appear to be very high in Delhi right now, relative to Mumbai’s.

If we take recorded fatalities at face value, Mumbai has had a higher fatality rate than Delhi: at the end of 2020 there were, officially, 86 Covid-19 fatalities per lakh population in Mumbai, as against 55 in Delhi. But during this last week Delhi has recorded a shocking 1,347 fatalities, as against Mumbai’s 361. These are the highest numbers this year for both cities, but Delhi’s current per capita death rate is more than twice Mumbai’s.

Moreover, as far as we can tell, Mumbai’s daily fatalities today remain below 2020 peak values; Delhi’s on the other hand are well above 2020 peak values. A caveat is in order here. Tracking deaths during previous waves has been complicated – unnecessarily and frustratingly – by both city administrations fudging their data. In both cities large numbers of early deaths were omitted from official counts, before later being added in via “reconciliations”. This means that some educated guesswork is needed to figure out when some of the fatalities occurred.

What can explain the surges?

What can explain the rapid spread of infection in these two hard hit cities? Here are two things we would really like to know:

  • What variants of SARS-CoV-2 are circulating in Delhi and Mumbai?
  • How many of the current infections are reinfections?

Data is lacking on both these questions. Because genome sequencing has been very limited, and data in the public domain is more limited still, we cannot be sure whether there is a story about variants lurking beneath Delhi’s and Mumbai’s alarming numbers. But it would help explain the data if the cities are succumbing to variants of the virus which have some advantage over previous variants.

Such an advantage could be if, for example, a variant is more transmissible, meaning that infection is able to spread more easily from person to person. Or if the variant is more easily able to cause reinfections in people who were previously infected by a different variant. The presence of such variants would certainly help to explain the explosions of infection or, more technically speaking, why R is so much higher than we’d expect.

It is even possible that different variants could be circulating in the two cities. Could this be behind the differences between how many deaths are occurring in the two cities? Or is Delhi’s very high death toll because some vulnerable sub-populations managed to stay relatively protected during previous waves and are now being hit hard?

Whatever we ultimately find out, received wisdom about Covid-19 needs updating. We need to junk the assumption that high prior infection rate protects a city against big surges. More than one year after the pandemic hit, with more than half the populations already infected, health infrastructure in both cities is stretched to breaking point. And tragedies are unfolding.

In Delhi, the best hope is that new measures to slow the spread will see rapid success, and cases will stabilise as in Mumbai. Otherwise a large number of avoidable deaths will inevitably occur.

Murad Banaji is a mathematician with an interest in disease modelling.