Yet he was worried online misinformation was leaving people with the wrong impression.
"I've heard friends of friends and seen people on social media asking questions about the vaccination status of cases, with the implication being that because vaccinated people are getting infected, what is the point of getting vaccinated?" he said.
"Rather than just complaining about this misconception to my family or on social media, I decided to use my mathematical expertise to help address these issues and illustrate why vaccination is important to prevent the spread of Covid-19."
In his analysis, Watson explored how rising vaccination rates changed the initial spread of Covid-19, along with the likelihood of a given infected person being vaccinated or unvaccinated.
As well, he wanted to find out what vaccination status meant for hospital risk.
Using what's called a stochastic model, he simulated an outbreak beginning with a single, unvaccinated case and unfolding over a period of 28 days.
After factoring in a range of variables, such as public health controls and increasing vaccine coverage, around 100,000 runs of the model left him with a clear picture.
It underscored the fact that, as the vaccination rate rose, the number of breakthrough infections and hospitalisations among vaccinated individuals did too.
"As vaccination rates increase, we expect to see more vaccinated cases simply because there are more vaccinated people," Watson said.
"Vaccinated individuals are less likely to be hospitalised than unvaccinated individuals as well as less likely to infect others."
Overall, the model showed unvaccinated individuals were about 3.3 times more likely to be infected - and 25 times more likely to be hospitalised.
On a population level, the difference was similarly striking.
"I used a conservative estimate that the vaccine is 70 per cent effective against infection. For a vaccination rate of 60 per cent of the total population [Auckland's current equivalent is around 74 per cent], the number of infections is only about 3 per cent of the number of infections in an unvaccinated population," he said.
"This is a much bigger decrease in infections on the population level compared to the individual protection.
"This illustrates the importance of people getting vaccinated to protect others as well as to protect themselves."
He noted the model had several key limitations: it didn't account for age distribution or testing, tracing and isolation of cases, it also assumed the cases were equally likely to interact with vaccinated and unvaccinated individuals.
"In reality, unvaccinated individuals are more likely to have unvaccinated contacts and so Covid-19 can spread very rapidly in unvaccinated populations."
Watson said the research ultimately illustrated the risk faced by under-vaccinated communities around New Zealand, at a time restrictions in Auckland were poised to ease.
"All over the world, we are seeing that Covid-19 is becoming a pandemic of the unvaccinated," he said.
"The Covid-19 vaccines are safe, effective and are our best chance of minimising infections and hospitalisations without resorting to large scale population level controls."
According to Ministry of Health data, people who had been fully vaccinated for at least two weeks before being infected have accounted for just 11 per cent of all cases in the Auckland outbreak.
Ministry of Health chief medical officer Andrew Connolly said as our vaccination numbers increase we could expect to see far fewer people who were so unwell they would need hospital care.
"As the number of people in New Zealand who are vaccinated increases, we will see a relative drop in the total number of cases," he said.
"However, because the total number of vaccinated people is greater than the number of unvaccinated people, we will see an increase in the number of cases among the vaccinated when both sets of data are combined and compared."
That was expected, he said, and was in line with overseas experience.
"What's important is to look at what is happening in each subset of vaccinated and unvaccinated people."
Connolly provided his own averages: if 1000 fully vaccinated people are exposed to Covid-19, about 75 of them, or 7.5 per cent, would catch the virus.
When 2000 fully vaccinated people were exposed to Covid-19, there would be 150 cases.
But when 1000 unvaccinated people were exposed to the virus, 500 of them would catch the virus.
When 10,000 people were exposed, the difference between a 50 per cent and 90 per cent fully vaccinated population would prove significant.
Modelling suggested 10,000 exposures among a half-vaccinated population could lead to 2875 cases and 263 hospitalisations, with all but 13 of those hospital cases being unvaccinated.
At 90 per cent coverage, however, those 10,000 exposures would result only in 1175 cases and 73 hospitalisations.
"Because vaccination rates are so high, a higher proportion of people in hospitals will have been vaccinated, about 32 per cent - or 50 unvaccinated people and 23 vaccinated."
Connolly added that vaccination also significantly reduced and slowed transmission in households and communities.
"A very recent study shows when a vaccinated person was infected they're nearly two out of three times less likely to infect unvaccinated households," he said.
"A vaccinated person who catches Covid has got around a 63 per cent less likely chance of transmitting to household.
"If you add in the fact that most vaccinated people don't get the disease, the modelling suggests a more than 80 per cent reduction in household transmission."
Watson's study follows earlier work that has similarly shown how cases among the vaccinated will climb over time as coverage rates rise.
"At the start of this outbreak, only something like 20 per cent of eligible people in Auckland were fully vaccinated – and now we're closer to 90 per cent," Te Punaha Matatini modeller Professor Michael Plank said.
"So, of course, we can expect that the proportion of cases that are vaccinated will have increased significantly over that period of time."
Plank said waning immunity from the vaccine also played a part.
"As time passes, immunity from the vaccine against getting infected does fade – and that, again, will contribute to an increasing proportion of cases being vaccinated. We can counteract this with booster shots."
