The number of patients in Devon hospitals with Covid has increased by about five times since early September.
NHS figures shows 250 people in hospitals around the county have tested positive for the virus.
NHS Devon is asking for support to help reduce the spread of Covid and the flu and is urging those eligible to get both vaccinations.
People are also being asked to stay away from hospitals and care homes if they have symptoms.
Higher Covid rates add to the already-existing pressures in the local health and care system, NHS Devon said.
Chief medical officer Dr Nigel Acheson said he appreciated the public's support and their patience with staff "at this very busy time".
He said: "Many people will be well aware of the pressures affecting the NHS and will want to do their bit to help."
Health bosses said people could also help by using the most appropriate service for their needs, including pharmacies and NHS 111.
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