He initially predicted a peak about 190 cases a day across the city's hospitals and amended that last month to about 400.
But actual daily case numbers had been as high as 533 this week.
Jackson said modelling Omicron was always going to be tricky because it was a new variant and New Zealand's situation was unique as the virus hit - it had a highly vaccinated population and was rolling out the booster.
"There were some assumptions put in around how much it would spread in such a situation and... the actual case numbers have spread faster than was expected," he said.
His modelling at the start of the outbreak gave three scenarios based on data from Covid Modelling Aotearoa.
The lowest scenario tracked like South Australia's outbreak, the middle like London and the highest like New York.
It was predicted that Auckland would be most like South Australia - but in fact, in terms of hospitalisations, it had surpassed even the New York scenario.
The modelling has been updated and Jackson hoped the city was about to peak.
It was hard to predict because it was much more difficult to know what the true number of community cases were now people were using rapid antigen tests and reporting their own results.
But the pressure on hospitals appeared to be no longer increasing, he said.
"It hasn't gone down but it's starting to slow a little. Maybe I'm getting hopeful but... those ED numbers... it looks like the people hitting the front of the hospital are starting to plateau a bit," he said.
Jackson's figures show as many as 45 to 50 per cent of children under 15 at Middlemore's emergency department have been presenting Covid.
Across all ages, there have been 35 to 40 per cent with Covid at Middlemore, 25 per cent at Auckland Hospital, and 20 per cent at Waitematā's hospitals.
But the Middlemore numbers had not increased in the past week, Jackson said.
The Northern Region Health Coordination Centre said 28 per cent of people at Middlemore's ED had Covid on Tuesday.
A doctor at an emergency department in the city, Dr Elspeth Frascatore, said she had been surprised at how fast Omicron had moved.
Frascatore, who represents the union, the Association of Salaried Medical Specialists, said EDs had been very busy, particularly because they also had staffing shortages.
"We are expecting this is going to be two to three weeks probably of this being pretty awful but we will get through this and get out the other side, but it's not necessarily going to be easy on us," she said.
While it was high pressure, every patient who needed urgent care was still getting it to a high standard, she said.
Jackson also models Northland's outbreak and said it was a few weeks behind Auckland, with currently about 11 per cent of people turning up to hospital with the virus.
