The rate of infection in Dudley has risen four-fold over the past week but is still far lower than the rest of the Black Country and Birmingham.
The latest data shows there were 16 new cases from July 21 to 27 - an average of five cases per 100,000 residents.
This is compared to four from July 14 to 20 - an average of 1.2 cases per 100,000 people.
However in the week when Dudley had 16 new cases confirmed, Sandwell had 106 new cases and a rate of infection six times higher than Dudley.
Sandwell is "halfway towards" a local lockdown as a result, while Wolverhampton has also seen a surge in the rate of infection.
Latest rates of infection in the region:
Average number of new cases per 100,000 people for the seven days to July 26.
Figures show rate for seven days to July 26 followed by equivalent figure for the previous seven days to July 19.
Data for the most recent three days (July 27-29) has been excluded as it is incomplete and likely to be revised.
Sandwell 32.4 v 23.2
Wolverhampton 15.3 v 5.0
Birmingham 13.1 v 12.6
Walsall 6.7 v 11.3
South Staffordshire 5.4 v 2.7
Dudley 5.0 v 1.2
Stafford 2.9 v 3.7
Among the increase in cases there are instances of spread within family households and Dudley’s director of public health is reminding people of the importance of following government guidelines to help prevent the spread of Covid-19.
Director of public health Bal Kaur said: "We are closely monitoring the data for Dudley and while our number of cases remains very low, we have seen a small rise over the last week, some of these within family households.
"With restrictions easing and us all now being able to see family and friends, it’s important to remember the virus has not gone away.
More Covid-19 coverage:
"It’s vital we continue to limit contact with people outside our own households or bubbles, we don’t meet in large groups and we follow social distancing and stay at two-meters away from others, where we can.
"If you have symptoms you must self isolate and get tested. If your test shows you have the virus you will be asked to protect the community by sharing details of your close contacts with the NHS Test and Trace service. This allows us to provide guidance to the contacts to slow the infection rate in the borough.
"While we have seen a rise in cases, it’s important to stress this does not mean we are close to a local lockdown.
"The numbers are still low in Dudley and I’d like to thank you all for your efforts in adhering to public health measures. However, we do need everyone to continue to play their part and follow government guidance to help control the virus and save lives.”