Infections are at the highest level since July but less than a third of eligible children have had the vaccine.
The virus is spreading rapidly among 10 to 14-year-olds, with 1,626 of the 6,144 new infections recorded in the week to October 15 occurring in that age group.
In total five to 19-year-olds accounted for 2,850 of the positive tests in that period.
Covid-19 is less dangerous for young people but it is feared spiralling infections in any age group could lead to a spike in hospitalisations and increased pressure on the NHS going in to winter.
Rates in over 60s are also increasing but at a far slower rate.
But the national booster jab roll-out – where people over 50 who are six months on from their second dose can get a third – has been slow and at the moment is not expected to be completed until March next year.
Overall, cases in Kent rose by 23% week-on-week while in Medway the increase was 14%.
Swale has seen a worrying 78% surge in cases, while Sevenoaks' 633 new cases means it is currently the area with the most infections per head.
There have been six deaths across Kent and Medway in the past 24 hours and 17 in the past week, a figure which has been relatively stable since September.
There are 77 people in hospital across the county, nine of whom are on ventilators.
Across the UK yesterday 179 people died and 49,139 tested positive. In the past week 820 have died, while 7,891 are currently in hospital and 850 are on ventilators.
The situation in the county mirrors what is happening across the country as health chiefs and scientists call for restrictions to be reimposed.
Health secretary Sajid Javid softened his stance yesterday and said while "plan B" – which would see work from home rules and mask wearing brought in – would not be brought in yet it is a possibility if cases don't go down.
The government has repeatedly ruled out another lockdown, business secretary Kwasi Kwateng "categorically" ruling one out in an interview yesterday.