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Pandemic Waves: Why Covid infections rise and fall

May 23, 2022

The wave is arguably the most illustrative and persuasive epidemiological concept to emerge from the pandemic. In this article, Dirk Meerkotter, looks at the concept origins and what insights can be gleaned from these data visualisations.

The waves off Cape Town’s Muizenberg beach have always been popular with local surfers, and when the conditions are right, the water is speckled with dozens of wet-suited warriors. Many plan their days around the tidal swell, and the discerning surfer will only set out if the conditions are right.

Since the start of the pandemic, many of us have become habitual Covid wave watchers and plan our activities around the peaks and lulls of the latest wave of infections. We have become so familiar with this inevitable rise and fall that we hardly stop to question the mechanisms that drive it.

From patient zero to pandemic

It is simple and intuitive enough to understand how we get from a single infection to multiple: Patient Zero infects a certain number of people, who in turn infect others. If an infected person, on average, passes the virus on to more than one other person, we quickly have exponential growth. A virus’ ability to spread is measured by a reproduction number or R number. If the R number is below 1, it means most infections are not transmitted, and the chain is quickly broken1

The R number is partially determined by the inherent transmissibility of the virus itself - the current Omicron variant, for instance, is more contagious than the earlier strains - but also by environmental factors and interventions that could slow the spread.

The interactive visualisation below, originally seen in The Washington Post, simulates a virus spreading in a closed system. The peak of the wave is formed as an increasing amount of infected dots infect even more. But as this is a closed system, the dots eventually recover and become immune. Any infected dot is more likely to bump into an already infected or immune dot than into a susceptible healthy dot. This visualisation is a simple example of an epidemiological SIR (Susceptible-Infectious-Recovered) model2 .

An epidemiological SIR (Susceptible-Infectious-Recovered) model.

Lockdowns and other interventions work by limiting the mobility of dots and, by association, the virus to come into contact with new susceptible dots. This slows the spread and “flattens the curve”.

The question then is not why infection waves rise and fall but rather why they recur. Despite our familiarity with the pattern, it is, in fact, something not clearly understood by epidemiologists. The simulation is not reality, and we’re not dots. 

As Harvard science historian, David Jones explains: “The impact of a pandemic depends on the interaction between the pathogen and the society, and these vary enormously”3

Painting seascapes

The pattern of rising and falling disease in a population was first noticed in the mid-19th century as a result of better data collection of disease trends4. The wave pattern was applied and noticed retrospectively for the 1918 Spanish flu (Early reports came from Spain, and the unfortunate misnomer stuck). The pandemic had a first mild outbreak followed by a lull and then devastating second and third outbreaks.

Line Chart showing deaths per person.

The recognition of the wave pattern was aided by the invention of line and bar charts in the late 18th century by data pioneers such as William Playfair.

Jones and Helmreich traces the early use of the wave metaphor to observations of disease in the British colonies and suggests that this framing of disease as a naturally occurring wave conveniently absolved authorities from taking responsibility for intervention and improving the healthcare of their colonial subjects.

As the field of epidemiology advanced however, the concept became more than a metaphorical or visual aside to liven up reporting and more of a predictive tool that helped shape our understanding of contagious diseases and inform our options for control.

The ups and downs of a Covid wave

New waves of infections are not caused by a single factor but rather by a combination of interrelated phenomena. Epidemiologists differ on the exact weightings but highlight variable transmission rates, virus mutation, waning immunity, sub-group isolation and human behaviour as the underlying mechanisms that drive the spread of contagions.

Variable Transmission Rates

The speed at which a virus might spread through a community is variable and context specific.  We are all familiar with the annual calls for flu vaccinations that we ignore. Influenza has a variable transmission rate based on season and tends to transmit more easily in colder months. The transmission rate of a virus can also be affected by the population it moves in and the interventions it encounters. It turns out your mother was right, and you can catch a cold from being cold.

Virus Mutation 

Much to the annoyance of fundamentalists, we have witnessed the evolution of the virus and seen the emergence of many variants over the course of the pandemic. The Omicron variant has a much higher R number than Delta before, and any infected person will, on average, infect more people. Many of the pandemic waves worldwide have been driven by new emerging variants.

Waning Immunity

Infection and recovery from a virus will bestow the patient with some immunity. However, the length of immunity depends on the virus. Immunity to any particular variant of SARS-CoV-2 has proven to be relatively short, and previous infection with one variant does not guarantee immunity to any other. 

Many countries have relaxed restrictions in the hope of reaching some form of herd immunity. This has proven to be a pipe dream in the case of Covid, as re-infection is not only possible but very common. While vaccinations are easing the burden on healthcare systems, they are not perfect, and time will tell how this will support long term immunity.

Sub-group Isolation

While you might have a diverse group of friends, we do tend to move in sub-groups of the broader population. Unless they’re singing at the local old-age home, primary school learners don’t often hang out with octogenarians. The population is not monolithic, and some groups might never cross paths. We can see some groups as closed systems which brings us closer to the simulation above. A wave of infection might start in a particular sub-group and fizzle when the limits of the group have been reached. 

Human Behaviour

Transmission rates, mutations, immunity and population sub-groupings are nuanced and complex phenomena but relatively simple when compared to the unpredictability of human behaviour.

A virus needs a lift and the myriad of interactions and activities that make up our daily lives, provide it with the perfect opportunity to travel and spread. 

It is by no means conclusive, but it is perhaps not a coincidence that waves in neighbouring countries tend to follow each other, as we can see in this comparison of countries in Western Africa using Africa Data Hub’s Covid Wave Watch.

We can also see that the waves of infection in Northern Africa (the first six countries) are usually out of sync with those in Southern Africa (the bottom five countries):

However, looking at different time periods and countries in the Covid Wave Watch chart, it is also striking how often even distant countries are in sync. This is perhaps a further illustration of the interconnectedness of the world and a reminder that there are virtually no closed systems. 

Lockdowns and other restrictions are put in place to mitigate the epidemiological consequences of being human and living in a society.

Breaking waves while making waves

Jones and Helmreich suggests the wave pattern has moved beyond a model of prediction to a tool of persuasion5

We are all familiar with the wave cycles. We discussed it over dinners that probably should have been cancelled and we measure the risk and reward of any social engagement depending on where it falls in a cycle.

It is a true testament to the complexity of human behaviour when we realise that the recognition of the wave ultimately affects the wave itself.

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