Officials confirmed three cases of coronavirus in West Yorkshire on Sunday and four new cases in England today, bringing the UK total up to 40.
Two patients are from Leeds who became infected while travelling to Iran while the third case, a woman from Ilkley, picked up the virus in Italy.
Leeds Teaching Hospitals has reassured patients that measures have been introduced to protect patients and staff in a message on the trust's website.
The trust said: "The NHS in Leeds and Public Health England (PHE) are extremely well prepared for outbreaks of new infectious diseases.
"The NHS has put in place measures to ensure the safety of all patients and NHS staff while also ensuring services are available to the public as normal."
Isolation pods have now been introduced at Leeds General Infirmary, St James's Hospital and Wharfedale Hospital to treat coronavirus patients.
The pods are intended to prevent the spread of the virus should further outbreaks occur in Leeds.
More than 11,750 people have now been tested for coronavirus in the UK and while most patients only have mild symptoms, Covid-19 appears to be much more deadly than seasonal flu.
Boris Johnson has warned that more cases could be challenging for the UK and urged people to take simple steps such as washing their hands to reduce the risk of infection.
Speaking at an emergency Cobra meeting today, the Prime Minister said: "We have also agreed a plan so that if and when it starts to spread, as I'm afraid it looks likely it will, we are in a position to take the steps necessary to contain the spread of the disease as far as we can, and to protect the most vulnerable."
On January 31, two people staying at Staycity Aparthotel in York became unwell and were the first to be diagnosed with the virus in the UK.
There were fears in Leeds the following week when medics in hazmat suits were spotted outside Vita student accommodation on Cross Belgrave Street.
The YEP has seen a message posted on Chinese social media app WeChat, appearing to show the woman's medical discharge summary.
It suggests that the woman was admitted to St James's Hospital and that it was the opinion of the infectious diseases consultant that she did not have Coronavirus.
MP Alex Sobel cancelled all his engagements in Leeds for two weeks in February as he self-isolated amid coronavirus fears.
The Leeds North West MP had attended the UK bus summit in London on February 6 where an attendee later tested positive for coronavirus.
Although he was at 'very low risk', Mr Sobel called 111 and self-isolated for two weeks and advised anyone with concerns to take the same approach.
Speaking during his isolation period, Mr Sobel said: "Public Health England gave the advice that I should take reasonable precautions.
"Right now I should be at surgeries with constituents. We thought it a reasonable caution to self-isolate until next Wednesday evening.
"I'm fine. I've got no fever. But as you can present after up to 14 days, I've taken these precautionary measures."
In Italy, which has the most cases in Europe, there are now 1,694 confirmed cases and 34 deaths.
Two schools in east Leeds issued advice after pupils and teachers returned from skiing trips in northern Italy during February half term.
Corpus Christi Catholic College in Halton Moor and Bishop Young Academy in Seacroft both sent letters to parents with the latest advice.
Neither trip had been to one of the 12 towns on lockdown in northern Italy, but PHE has asked that anyone who has been north of the Italian city of Pisa to stay at home if they do develop flu-like symptoms.
Staff and students were advised to attend school as normal unless they began to feel unwell.
It is not yet known how the virus spreads from person to person, but similar viruses are spread through cough droplets.
Boots have limited hand sanitiser sales in Leeds Station due to shortages amid Coronavirus fears and customers are warned they can only purchase two products per person per day.
NHS advice is to avoid catching and spreading germs by washing your hands often and avoiding close contact with people who are unwell.
Self-isolation is only necessary if advised to by the 111 online coronavirus service or a medical professional.
For more advice on preventing the spread of the coronavirus visit this page.