Why do pandemics come in waves?

The ongoing second wave of the COVID-19 pandemic in India has been devastating in its reach and impact. Among my friends, family, and acquaintances, I doubt there is a single person who hasn’t been affected directly. Some had the disease themselves; others saw a loved one suffer from it, and more than one ended up losing someone dear to them. At the time of writing this, while daily case numbers have declined to a fraction of what they were in May 2021, 35000-45000 cases are still reported daily in the country, and the threat of an even more severe third wave looms on the horizon.

We have learned a lot about viruses and pandemics in this past year, perhaps much more than we ever wanted to. We are overwhelmed by the information bombarding us every hour through our TV channels and our news feeds, inevitably slipping into our discussions with family and friends. Yet, even with such an incessant deluge of information everywhere we look, certain key questions remain unanswered. As time goes by, these build up and accumulate in the back of our brains, slowly adding to the dull sense of dread that we are all familiar with by now.

For example, how do we know when one wave has ended and another has begun? Why does the timing of the waves differ so much from country to country? How many more waves will be there before the pandemic is over? How will we know when the last wave has come, and how sure will we be that the pandemic is at an end? And for that matter, why do pandemics come in waves at all?

Unfortunately, for some of these questions, the reason we don’t have clear-cut answers is simple – we just don’t know yet. Scientists have had a little more than a year and a half to observe the novel coronavirus in action, which is too short a period to make truly accurate predictions about how the disease may evolve. We are also hampered by the fact that there haven’t been many pandemics of this scale in our recorded past for us to draw reliable insights from – basically, we have too little data. 

Going back a century

However, this does not mean that we have no clues at all. The idea of waves was first popularized during the rather inaccurately named Spanish flu pandemic of 1918-19. Sometimes dubbed “the mother of all pandemics”, this influenza outbreak resulted in an estimated 50-100 million deaths worldwide, with almost 500 million people being infected. In contrast, reported total deaths due to COVID-19 recently crossed 4 million, while about 190 million people have been infected so far.

masked woman 1918
A woman in a mask in Washington, D.C., during the influenza pandemic of 1918 (Credit: Unnamed photographer for National Photo Company, Public domain, via Wikimedia Commons)

Keep in mind that the total population of our planet was only around 1.8 billion in 1918 and long-distance travel was much more uncommon. Back then, the world was still reeling from the effects of World War I, which was still ongoing when the Spanish flu pandemic started (and probably contributed to its spread). And it would be another dozen years or so before the influenza virus would even be discovered.

The Spanish flu pandemic, which likely originated in the US, had three distinct waves during 1918-19.  Most of the deaths occurred during the second and third waves, following premature celebrations and easing of restrictions after the first wave had died down.  While we have had the chance to prepare better this time around, not the least due to advances in medical technology, the risk of history repeating itself is too high to ignore. The second wave during the 1918 influenza pandemic also disproportionately affected young men and women, who usually tend to be the most resilient demographic group when it comes to infectious diseases.

The experience of the 1918-19 pandemic taught us three things. First, a temporary downturn does not mean that we are out of the woods. The disease may yet return, and the toll might be more devastating than before. 

Second, most of those infected by the virus survived in 1918-19, even in the absence of modern medicine and accurate scientific knowledge. However, it was impossible to predict exactly who would recover from the infection and who would not. Mortality rates also varied widely from population to population. The same holds true today – overall low death rates do not mean that any of us are individually “safe” from the disease.

And the third, and perhaps most important, lesson is that the disease may drastically change its nature between waves. Knowledge that we have gained from observing the epidemic during its initial stages –who it affects, how quickly it spreads, what proportion of patients it kills etc. – may no longer be valid once the virus returns during a subsequent wave. And this is a scary proposition to wrap our heads around.

1918 waves
Three pandemic waves: weekly combined influenza and pneumonia mortality, United Kingdom, 1918–1919 (Credit: Centers for Disease Control and Prevention, Public domain, via Wikimedia Commons)

The mathematics of infectious diseases

Before diving deeper, let’s note here that the term ‘wave’ is not precisely or mathematically defined in the context of pandemics. Attempts have been made to create a formal or a working definition, but these have not yet achieved scientific consensus. As a result, many experts differ in their opinions of what constitutes a wave, and opinions vary across the world regarding what stage of the pandemic a particular country may be in at a given moment.

However, certain key features are commonly accepted. From looking at any chart of daily new infections over time, we can see that a wave usually consists of a succession of ‘peaks’ and ‘valleys’, with the emergence of new cases at their highest on top of the peaks and their lowest at the bottom of the valleys.

The classical model of epidemic spread is called the “SIR” model, and it looks like a hill – an upward surge of infections, followed by a peak, and finally a steady decrease. It depends on three parameters – (1) S – The number of people in a population susceptible to an infection, i.e. those who haven’t contracted the infection yet but may do so in the future (2) I – the number of people who are currently infected, and (3) R – the number of people who have recovered from the infection (and are presumed to be resistant to contracting it a second time, though this is far from certain in COVID-19’s case). As time goes by, the number of infected or recovered people rises while the number of susceptible people falls, and an end to the epidemic comes when there is no one left to be infected.

sir model
An animation of the SIR model showing the effect of changing the infection rate (“flattening the curve”) (Credit: Phrontis, CC BY-SA 3.0 , via Wikimedia Commons)

While the most basic form of the SIR model is great for describing how infections spread in an isolated population, it does not take into account reinfections, vaccinations, access to medical technology, migrations, or other human behaviour.  It is also not sufficient to explain the wave nature of pandemics (though attempts have been made).  

Another factor to keep in mind here is Ro (R-naught), which many of the readers may be familiar with from TV interviews, webinars, and news reports since the early days of the pandemic. Taken very simply, Ro represents the average number of people that a single infected individual can infect.

Let’s imagine there are only 10 infected people in a population, and each of them passes on the infection to two of their family members or friends. So, we are left with 30 infections, the 10 original cases (called primary infections) and 20 new cases (called secondary infections). The Ro in this case would be 20/10 = 2. These 20 newly infected individuals can now infect 40 more, and thus the total number of infections rises exponentially. As long as Ro is above 1, the rate of new infections keeps rising. If Ro falls below 1, however, the rate of new infections in the population goes down.

So, why waves?

As far as we understand it, the reason for the wave nature of epidemics (or pandemics) is linked to both human behavior and virus biology. Viruses may survive better in certain temperature and humidity ranges, which allows them to spread further when favorable conditions are met. The seasonal flu virus in many western countries appears to behave this way, usually disappearing in the summer and returning in the fall and winter.

Unfortunately, it appears that the novel coronavirus is quite adaptable to a wide range of environmental conditions, allowing it to spread unchecked in both warm tropical countries (like India and Brazil) and cold temperate ones (like Italy and UK). Therefore, the second major driver of waves becomes more important here – our own behavior and activities.

Human beings are social creatures and we are naturally averse to being cooped up. The previous year has created extraordinary conditions and it is perhaps understandable that our tolerance is at its limit. As a result, as soon as daily case numbers start going down, people start moving. As restrictions are eased, more places are opened, and very importantly, as we see our peers, family, and others in our social circle start to step out and mingle, the urge becomes overwhelming to do so ourselves. And as human movement and interactions increase, so does the probability of the virus spreading, R­o increasing, and eventually, a new wave arriving.

At the time of writing this, many European countries have seen three distinct COVID-19 waves. Some countries which took early steps to counter the pandemic, e.g., New Zealand and Singapore, have seen only one. USA, Brazil, and India have broadly seen two waves each – however, it is difficult to delineate waves in these countries, since the number of daily new infections never really came down to insignificant levels between waves.

So, it is possible that the USA is still in its extended first wave while India is riding out its second.  Misreporting and insufficient testing have also taken their toll on research into the dynamics of COVID-19 infections. While vaccination numbers have been steadily increasing, experts agree that herd immunity is still some distance away.

Let us consider vaccines for a moment. As of the time of writing this, there are at least six COVID-19 vaccines in the market that have received regulatory approval in at least one country. It is difficult to overstate how incredible an achievement this is.

Most vaccines take about 10 years to go from the early research stage to obtaining regulatory approval and reaching the market. Until now, the fastest vaccine to be developed on record was the Mumps vaccine in the 1960s, which took about four years. Contrast this with the fact that the Pfizer COVID-19 vaccine, one of the first to receive regulatory approval against the coronavirus, was developed in a little less than 11 months.

And as of 21 July 2021, according to Our World in Data, 3.7 billion doses of vaccines have already been administered against COVID-19. While only a small proportion of the earth’s total population has been fully vaccinated (with just 1.1% of the population of low-income countries having received at least one dose), it is an incredible achievement all the same.

But this effort will go in vain if, in between waves, the virus mutates to become resistant to the vaccine. This is not a far-fetched hypothesis. This is the reason why it is almost impossible to create a vaccine against HIV and why seasonal flu vaccines need to be updated every year. And the more the number of people who get infected by the virus, the more likely it is that the virus will mutate. Every one of the current variants has emerged this way. The alpha (UK) variant which was first detected in November 2020 was at least 40% more transmissible than the original variant, while the delta variant, which emerged in India during the second wave, is possibly 50% more transmissible than the alpha variant.

And the more we allow the virus to spread, the more likely it is that we will be getting a vaccine-resistant strain, which will give rise to further and further waves.

camp funston
Camp Funston, at Fort Riley, Kansas, during the 1918 Spanish flu pandemic (Credit: Armed Forces Institute of Pathology/National Museum of Health and Medicine, distributed via the Associated Press, Public domain, via Wikimedia Commons)

It is important to state here that social distancing, masking, working-from-home, vaccination etc. are not options for everyone. There are those who are compelled by economic reasons to risk their lives every day as well as those who cannot be vaccinated for medical reasons. For those of us who have the option to access these options, it is a privilege. Yes, it is restrictive. But it is the only way we can make sure that we are not putting the lives of all those at risk who don’t enjoy the same privilege.

Pandemics do end. COVID-19 is not the first pandemic in human history, nor will it be the last. The Spanish flu virus eventually mutated and became the seasonal flu virus that persists to this day, much less dangerous than its original form. It is likely that a similar fate awaits the COVID-19 virus. However, our aim should be to minimize suffering and the loss of human life as much as possible. In doing so, perhaps we can push the next wave as far back as possible until perhaps a time comes when one does not arrive at all.


Note 1: This article is dedicated to my grandfather, Biswanath Chowdhury, who succumbed to COVID-19 in December 2020.

Note 2: A version of this article was first published in Bandhan, a bilingual annual magazine.

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