That is according to NHS officials who have also said it is crucial that vaccinated people continue to follow coronavirus rules to safeguard those still waiting to be protected against the disease.
This is because there is no evidence that any of the current vaccines can completely stop people from being infected - which also has implications for hopes of coming out of lockdown.
Amanda Bloor, accountable officer at NHS North Yorkshire Clinical Commissioning Group, said there was some hope that the county may be "starting to turn a corner" as the vaccine roll-out progresses but added infection rates and hospitalisations would not decline rapidly anytime soon.
Speaking at North Yorkshire Local Resilience Forum briefing on Wednesday, she said: "The more people that have the vaccine the quicker the impact will be felt. That's why the programme is targeting those who are most at risk of contracting Covid and suffering severe harm and death.
"We have made really good progress but everyone who receives their first dose still needs to follow the government guidance.
"Protection from serious illness starts from around two to three weeks after the first vaccination and we are still in the process of gathering evidence around whether that vaccination actually prevents passing onto others."
Prime Minister Boris Johnson last week said he hopes England's lockdown will begin to ease on 8 March but this "depends on lots of things going right" - including the vaccine roll-out.
In North Yorkshire, all care homes have now been offered vaccines apart from one where a significant Covid outbreak has meant it was unsafe for vaccination teams to enter.
Mrs Bloor said more over 70s were also now receiving their first round of jabs and that the county remained on target to vaccinate all top four priority groups by 15 February.
Sue Cawthray, chief executive of care charity Harrogate Neighbours, said she was "delighted" that the county reached the milestone of vaccinating all available care homes but warned "we are still not out of the woods yet".
She said: "In these challenging times we are urging everyone to continue to follow the advice and guidelines set out by the government.
"There is still a chance you might still get or spread coronavirus even if you have had the vaccine and there are no guarantees as to what protection is offered from the first dose alone, so we need to ensure that until the second dose is rolled-out we put the safety of the most vulnerable people and those who care for them first.”
By Jacob Webster, Local Democracy Reporter