The busy road's being made two lanes in both directions between Segensworth and Titchfield - it's due to take 18 months.
Norovius Outbreak At Poole Hospital
People are being asked to stay away if they have had sickness or diarrhoea in the past 72 hours.
It's after an outbreak of norovirus at Poole hospital.
Two wards and an elderly assessment unit have been affected and means there are some visiting restrictions.
Chief operating officer Mary Sherry said: "We're asking the public to help us ensure we can run services as smoothly as possible by not visiting at all if they have had diarrhoea or vomiting, or been with someone who has, in the past 72 hours.
"When visiting anywhere in the hospital only essential visitors should attend. We know that if we can reduce the number of people coming in and out of the hospital we can significantly affect our ability to limit the virus's spread."
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