It is understood that the proposals were circulated to Executive ministers late on Thursday evening and Mr Swann will be seeking their approval.
It remains unclear when ministers will meet to consider the proposals.
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These latest proposals suggest that employees will be advised to work from home where they can and that employers should support this where possible.
“This should be communicated in such a way to make it clear that if a person worked from home when Covid-19 first arrived in Spring 2020, then they should be working from home now,” the document recommends.
Mr Swann’s proposals also suggest a “scores on the doors” scheme, similar to those in place for food safety standards, that would see the development of a “Covid score” for businesses based on an assessment of the measures they have in place and their compliance with public health regulations.
The document also warns that compliance with mask wearing and the use of face coverings is insufficient in Northern Ireland.
It states that compliance also remains sub-standard on public transport.
“Enforcement needs to be strengthened and action taken against those who are non-compliant, otherwise the public will see compliance as unimportant and optional and we will not secure the benefit which the wearing of face coverings offers,” Mr Swann warns in the document.
In the proposal, the collection of customer and visitor information by businesses is described as “patchy at best”.
Mr Swann also told Executive ministers that he plans to introduce a change in how the close contacts of confirmed Covid-19 cases are managed, with changes expected to relate to the testing of close contacts.
The move follows Wednesday’s decision to introduce mandatory Covid certification entry checks across the hospitality sector in Northern Ireland.
It is understood Mr Swann is proposing that the Assembly be given an opportunity to scrutinise the Covid certification scheme before enforcement begins in the middle of December.
The acceleration of the booster programme, announced on Thursday evening by Mr Swann, will see enhanced efforts to reach those who have yet to get a first jab, particularly younger people.
GPs and community pharmacies are set to play a key role, with dedicated vaccine hubs also being operated by the region’s health trusts.
The various different measures are being rolled out in response to surging transmission rates in the region and amid warnings that ministers may face the prospect of reintroducing more severe restrictions ahead of Christmas if the current wave is not brought under control.
“I am very pleased to see the rollout of boosters accelerating,” said Mr Swann.
“More than 260,000 of our citizens have now had boosters or third doses and this number will continue to climb significantly.
“People are still coming forward for first doses and there are indications that demand for first doses is increasing again. Within the past week alone, community pharmacies administered in the region of 1,000 first doses to people aged 18 and over.
“The planned programme of additional walk-in clinics will help meet demand for first doses, as well as for boosters.
“Overall, the vaccination programme provided 97,000 jabs in the last week. We owe a great debt of gratitude to everyone involved in making this happen.
“It should be remembered that this vaccination programme is being delivered by a health and social care system experiencing the most sustained and severe pressures in its history.”
On Wednesday, a majority of Stormont ministers backed the Covid certification scheme despite DUP opposition.
It will see legal enforcement of coronavirus status entry requirements for nightclubs, bars, restaurants and a range of other settings from December 13.
While the four DUP ministers voted against the vaccine passport proposal, the party did not deploy a cross-community voting mechanism that could have blocked the introduction of certification in the region.
However, the DUP has called for a vote in the Assembly before the policy is introduced. Previous Executive decisions on Covid-19 rules, including lockdowns, have been subject to retrospective votes in the chamber, usually weeks after the measures have been rolled out.
A two-week grace period will then be in operation with enforcement action beginning on December 13. Venues that do not comply with the rules could face initial fines of £1,000.
While the DUP opposed the move at the Executive table, there is evidence of differing opinions within the party.
Some prominent members, such as First Minister Paul Givan, MP Sammy Wilson and former economy minister Paul Frew, have been highly critical of the policy but others, including MLA Pam Cameron, have indicated their backing for the measure.
On Thursday, DUP MLA Christopher Stalford said certification was a “distraction” that would not alleviate the pressures on the health service.
He said increasing booster rates and diverting resources to domiciliary care packages would have much more impact.
“Covid passports are not going to stop ambulances queuing outside EDs,” he said.
“We need a proper plan to do that. One that deals with root causes of why our hospital staff are under pressure. One that ensures medically fit to be discharged people can get a care package.”
Under the compulsory certification scheme, people wishing to gain entry to designated venues would need to demonstrate evidence of Covid-19 vaccination, a negative lateral flow test result, or proof of a coronavirus infection within the previous six months.
Concerns have been raised that the lateral flow test result option could be open to abuse as the process relies on individuals self-reporting a negative result.
Chief scientific adviser Professor Ian Young conceded the potential for results to be manipulated but he expressed hope people would act in the public good.
“It is possible for that system to be manipulated and for individuals to give a false result,” he told BBC Radio Ulster.
“That is something we will be keeping a very close eye on.”
He added: “I am confident that the Northern Ireland population, understanding the severity of the situation that we find ourselves in, will want to the right thing…will want to protect themselves and other people from this virus.”
A modelling paper from health officials presented to the Executive this week warned passports may not be enough to suppress rapidly increasing Covid case numbers, which have surged 23% in a week, and that “more severe restrictions” may need to be considered in mid-December to avoid hospitals being overwhelmed.
The deaths of a further six patients who had previously tested positive for Covid-19 in Northern Ireland were reported on Thursday along with another 1,681 positive cases of the virus.
On Thursday morning, there were 419 Covid-positive patients in hospital, with 34 in intensive care.