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Education chiefs have been urged to consider imposing a circuit-breaker in schools to stem the spread of coronavirus.
Labour councillors in Medway say there needs to be a "clear plan to mitigate system-wide pressures" being felt by rising infections.
Every secondary school in the Towns has been affected with at least one positive case either a staff member or pupil, the group says.
More than half of the 101 schools in the Medway area have reported cases with three secondary schools – The Hundred of Hoo Academy, the Howard School in Rainham and Strood Academy – closing for two weeks after a spike of cases.
Latest figures show 53 schools – 20 more than the previous week – were reporting at least one coronavirus case as at 5pm on November 18.
Attendance rates have dropped with 83% of primary age children in school at 5pm last Thursday, November 19 and just 57% in secondary schools.
The figure does not include children learning from home.
More than 4,000 pupils are self-isolating at home and being taught remotely.
Cllr Clive Johnson, the Labour opposition spokesman for children's services, has written to the Regional Schools Commissioner for the South East suggesting the impact of Covid-19 is hitting schools' ability to "deliver effective education" in the current circumstances.
He said: "The hard work of our schools and teachers in order to stay open cannot be overstated, and we should be extremely proud of how our educational community has risen to these unprecedented challenges.
"Despite this hard work to maintain standards, as more students and teachers test positive and increasingly substantial numbers are unable to attend school, it raises questions if schools are in a position to deliver effective education in these circumstances.
"This is an educational issue but one with clear public health consequences.
"Medway Maritime Hospital is evidently under significant strain, and minimising transmission to the wider community via schools is an important aspect of this."
Cllr Johnson noted how many pupils in Medway live in Swale where cases soared to 631.7 cases per 100,000 people in the week up to November 18, making it the highest in England.
He added there needed to be a focus in Medway on control the rate of infection in schools and across the community which would reduce the strain on the health service and avoid strict local lockdowns.
He wrote: "This could, for instance, include a system-wide closure of schools within Medway to provide a circuit-break with appropriate provision for students, including key groups."
Medway Council, the local education authority, has remained tight-lipped and would not be drawn on whether it is considering telling schools to close.
Individual head teachers are responsible for deciding whether to close their school.
It follows comments by Kent County Council's education director Matt Dunkley last week, who said it would be "tough" for schools to stay open until Christmas.
Cllr Martin Potter, Medway Council’s portfolio holder for education and schools, said: “The health, safety and wellbeing of children, teachers and school staff is of the utmost importance and schools have robust plans in place if there is an outbreak at their school.
"Throughout the pandemic we have worked closely with Public Health England to offer advice and support to Medway’s head teachers and we will continue to do so.
"Every school is different and head teachers are best placed to make decisions about their school.
"Children who have been sent home to isolate are encouraged to continue their learning with many schools offering online lessons.
“I would like to take this opportunity to praise Medway’s children and their parents and carers who have had to adapt quickly to the changes this year.
"It is also important that we recognise the incredible work of school staff across Medway during these challenging times."