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Each class of virus has an intrinsic rate of mutation.

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That is not constant, so "intrinsic" isn't really the best choice of words there.

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Rhinoviruses mutate more quickly than influenza, which in turn mutate more quickly than coronaviruses.

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Preface each with "some", and the entirety with "to our current knowledge".

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Widespread vaccination, by reducing the number of actively infected patients, will reduce the rate of emergence of new strains.

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Follow each with "temporarily"