It was confirmed earlier this week that Wakefield was one of 66 local authorities to have expressed an interest in receiving the new types of tests, known as lateral flow tests.
The tests can give results in as little as 15 minutes, and are currently being used as part of a mass testing pilot in Liverpool.
The Department of Health and Social Care said they would provide 10,000 of the tests to more than 50 local authorities in the coming week, with further allocation in future weeks.
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And Anna Hartley, Wakefield's director of public health, has now confirmed plans to meet with the government to discuss the potential roll-out of the scheme in the district.
Ms Hartley said: “We are currently exploring a range of options to reduce Covid-19 cases in the Wakefield district.
“One of the options is mass testing. We have expressed an interest in exploring this but want to understand what lessons can be learnt from the experience in Liverpool and other areas before progressing any further.
"We would like to explore how we could use a smaller, more targeted approach for high risk populations. We will be meeting with ministers on Friday to discuss this and will then consider our approach.
“We are also currently prioritising our efforts into establishing an effective local test and trace programme and, following the positive news about the potential availability of a vaccine, we are working closely with NHS Wakefield CCG colleagues to ensure that when a vaccine is available, we have the mechanisms in place to roll it out as quickly as possible.”
What is the current rate of infection in Wakefield?
A total of 10,200 people have tested positive for Covid-19 in the Wakefield district to date, up from 8,457 at the start of the month.
The rate of infection in the district currently stands at 499 per 100,000, more than double the national average of 239 per 100,000.
Since March, 421 people have died at hospitals run by the Mid Yorkshire Hospitals NHS Trust within 28 days of a positive Covid-19 test.
The Trust is currently dealing with its highest ever level of Covid-19 patients, and has been forced to close a number of operating theatres to free up staff to care for virus patients.
How are the tests different than the current system?
The new coronavirus tests differ from the current system in two ways.
First, the tests can provide results within an hour, and without needing to be processed in a lab.
Second, they will be made available to everyone who lives or works in an area, regardless of if they have symptoms of the virus.
The current testing system, which is available only to those displaying symptoms of the virus, involves booking tests in advance and waiting several days for a result.
A DHSC spokesperson said: "Proactively testing asymptomatic individuals will help identify those who unknowingly have the virus and enable those who test positive and their contacts to self-isolate, which can help drive down the R rate locally and save lives.
"This is crucial to break the chains of transmission of the virus and to support critical industries, key workers and institutions."
Since the beginning of the mass testing scheme in Liverpool last Friday, more than 23,000 people have been tested for the virus, with 154 positive results.
In line with the national testing system, anyone who tests positive must self-isolate along with their household.
Any recent contacts will be traced and advised to self-isolate.
Eligible individuals who test positive – and contacts who are required to self-isolate – will be entitled to the £500 Test and Trace Support Payment in the same way as a regular swab test ordered through NHS Test and Trace.
Who else will be taking part in the scheme?
More than 50 local authorities have signed up for the scheme so far.
Calderdale, Hull, Manchester and Darlington are among the areas expected to be granted an initial 10,000 rapid tests next week.
But speaking earlier this week, Leeds City Council confirmed it had not volunteered to take part in the scheme.
Prior to the testing being rolled out in Liverpool, Leeds City Council said last week that it was waiting to see how effective national pilots are to answer some of its concerns before making a decision on whether Leeds will volunteer to take part in the pilot.
They said their concerns included the implications of false positive and false negative results, the impact on workforce capacity, how tests will be administrated and link with Test and Trace and the capacity to effectively contact trace positive tests.