In the past 14 days some 28 cases of coronavirus have been confirmed in the town, which is "significantly higher" than was expected, and health bosses are also expecting it to rise again.
But a local lockdown situation such as in Leicester is not yet being considered, although the situation is being monitored, health bosses confirmed.
Sandwell Council public health experts are working with people in the area, businesses and community venues to make sure safety guidelines are followed.
Director of Public Health Dr Lisa McNally said the infection has been affecting multiple people in the same home.
She said: “The numbers are changing all the time. We have seen 28 cases in the last 14 days which is significantly higher than we would expect based on previous figures and it is changing all the time so we expect it to rise again.
“A pattern is emerging showing the infection affecting higher numbers of people in a small number of properties, two, three and four people sometimes in one household – often in multi-generational households - rather than lots of single cases across a lot of households.
“I know it isn’t easy but it’s very important that if someone is infected, they isolate themselves from the rest of their household as much as they possibly can, especially from elderly people.
“This rise in cases reminds us that the virus hasn’t gone away. We can’t afford to drop our guard. If we experience symptoms then we must self-isolate at home and get tested. Anyone in the same household also needs to self-isolate. Doing this saves lives.
“We can protect ourselves and those we live with by keeping at least one metre apart from others. Wearing a face covering when on public transport or when shopping also reduces the spread of the virus.
“We are not at a point where we are looking at a ‘lockdown’ situation like in Leicester. But we will keep monitoring the situation carefully and we really need everyone to follow the guidance.”
Sandwell Council Deputy Leader Councillor Maria Crompton said: “We are working very hard, using our local knowledge, and getting in touch with local venues to remind them to be vigilant.
“But we need everyone’s help, so please follow the advice from our public health experts.
“Anyone needing urgent medical help should always contact 999 or NHS 111.”