We had a tough November/December with many kids off or being sent home with an illness with extremely high temperatures last year. (Plus Noro, plus tonsillitis). Because the instant the thermometer showed at 39/40, they were sent home and were kept home (as they were too ill to go out and about), by the last week of term, the chaos had pretty much dissipated and only a handful were off.
By New Year, some of them, including those who had already been unwell, had come down with something else - a few were admitted to hospital over New Year.
Some came back to school and were sent home with that slightly different raging fever and other symptoms (such as a cough) by the end of the first week.
The second week saw large numbers of students and some staff off. The third week saw staff absences at an all time high - including me, who had gone through November and December in close physical contact and proximity with all those who needed to go home completely unscathed.
I assumed that the first wave was influenza. I don't know what the second one was, but it was fairly obviously brought into school by kids who had caught it just around Christmas, incubated it over the next week and then, once in school for the first week in January, the virus tore through the site over the next three weeks, affecting students and staff - I even caught it, despite going through handling every single student in November and December without a single issue. And I was off for over a week with it.
In terms of reducing January illness rates, I think it would make sense to delay the start of term, as then if somebody caught a virus, it would have time to pass before coming in to school.
However, that doesn't mean it solves everything. So I am not expecting it. I'm not looking forward to January.