# How is a virus like a firework?

There are some key descriptors that tell you the potential of a virus, like COVID-19, to spread. I thought I would have a go at elucidating these numbers using the analogy of fireworks.

The R number, or reproduction number, tells you how many people each person is spreading COVID-19 to on average. Or, if there was a bunch of fireworks lying on the ground, if you let one firework off, how many other fireworks are ignited as a result? Chris has direct knowledge of this. When his parents were holding a cocktail party when he was 9, he was socialising with the children of guests in the study. He pulled out a box of fire crackers and, for fun, lit one and threw it into the box to see what would happen. A lot of noise and smoke happened. He has a distinct memory of opening the study door, exposing a bunch of frightened children and a cloud of black smoke descending the staircase to the living room. Chris went down the stairs to face the music in a coil of smoke.

Pandemic modellers and epidemiologists use two R numbers. There is R0, which describes what happens if there is no deliberate control of a virus, or if you just let the firework go off and see what happens. The R0 for Delta is estimated at around 6 i.e. one person, on average, infects 6 other people. However, most countries are using active measures to reduce spread of COVID e.g. vaccines and masks. These measures reduce the reproduction rate. That’s a bit like letting your cracker off but putting it on the other side of the room from the box of crackers. The reproduction rate you see when restrictions are in place is called Re. The aim is to get Re to less than 1 because if every person infects, on average, less than 1 other person, the virus will die out in the population.

Then there’s the K number; I only learned about K numbers recently. The R number says how many people one person infects on average. But people aren ‘t all average. The K number tells you whether transmission of a disease is caused by few of the infected individuals, or many of the affected individuals. The K number can be any number up to infinity, at which point everyone infects everyone else equally.

From a firework point of view, is every firework equally likely to set other fireworks off? A Roman Candle might be great at showering sparks equally over a bunch of lined-up fireworks, a rocket heads away and has nothing to do with other fireworks until it falls to earth and a dud firework just fizzles out and does nothing. Of effective fireworks, I particularly remember some in Sulawesi when we were cycling there. These fireworks spun around rapidly on the ground once ignited, spreading green sparks and whining. They stopped spinning and went dark then, for a couple of seconds, nothing happened, next there was a very loud bang. I thought they were very funny but it didn’t seem like most people enjoyed the surprise.

Back to the K number – SARS 2003 had a K number of 0.16, while measles has one of 0.22 and seasonal influenza has been documented as ranging from 2 to 53. SARS-CoV-2 supposedly has a K number around 0.1 (around 20% of people cause 80% of cases); I haven’t managed to find anything comparing the K number of Delta with other variants. Having a small K number is both good and bad. A whole lot of people act like dud fireworks, not spreading virus to anyone. However, a small number of people are Roman Candles, spreading virus widely in ‘superspreading’ events, like the church cluster in Auckland currently. If you get lucky, and none of your infected people are a superspreader, then infection is easily contained; if you are unlucky…then containment is not so easy.

Generation time is another critical feature of infectious diseases – how long does it take from when one person is infected until they create infection in another person? Or, taking the firework analogy, how long from when the first firework starts shedding sparks until another firework is lit and starts sparking? This is very difficult to measure for infections – we don’t know when someone is shedding virus, we only know once they display symptoms of the illness; so we use the serial interval, as the time between when one person displays symptoms and someone they infect displays symptoms. We use serial interval as a proxy for generation time.

One of the reasons we don’t try to eliminate seasonal influenza, is because its serial interval is fast, at about 3 days. Rapid spread makes it difficult to suppress a disease because it may have already infected a considerable number of people before someone presents with symptoms and gets tested. The original strain of COVID-19 had a serial interval of around 7 days, while it looks like Delta has a serial interval of 4 days. Delta can outrun contact tracing. As Sydney found, by the time you identify a case you need to be contacting people two steps away from that case – you need to be contacting the contacts of the contacts.

Here’s a picture of how the higher R0 and lower serial interval is making Delta a challenge for New Zealand. On the left are the total cases identified in the first 9 days of the 2020 outbreak in New Zealand, once we started documenting cases regularly. On the right are the total cases identified in the first 9 days of this 2021 outbreak (the computer is determinedly chopping off numbers on the left, but the scales in the two graphs are the same) . In 2020 it actually took 27 days from the very first case for New Zealand to reach 192 cases, in 9 days we have 209. For all the world scoffing at New Zealand locking down at the sign of a single case of COVID-19, if we are to be on an elimination pathway, that was the only thing to do.