Due to the pandemic, more people are opting to stay in the UK for holidays which means visitor numbers to the Lake District are up.
Colin Cox said tourism also cannot explain the spike because the South Lakes area, very popular with visitors, has got the lowest rate in Cumbria.
"I think it's a courtesy that if you're visiting somewhere else it's good to take a lateral flow test."
There were 1,399 new cases in Cumbria in the week ending August 18, up from 1,266 five days earlier and 1,056 in the week ending August 6.
He said the key point is for visitors to take a test before travelling and for tourists and residents to remain vigilant and continue to take precautions
Mr Cox said: "We're not actually seeing a lot of transmission that we're pinning down to tourism at the moment, but obviously the virus does travel around the country with people.
"I think it's a courtesy that if you're visiting somewhere else it's good to take a lateral flow test before you travel so you're not part of that spread."
Public Health Director Colin Cox addresses the growing problem of littering in the Lake District.
Cox also urged visitors to 'respect the countryside' after a spate of littering and fly-camping incidents reported across the UNESCO World Heritage Site over the summer.
He said: "When you come to Cumbria, respect to the countryside. We've got lots of problems which is causing substantial problems that are not covid related.
"So, please come to Cumbria, but behave respectfully and behave responsibly when you're here."
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