But luckily most of the contamination happens through cough, so that these people that don't show symptoms are also less contagious.

And some case studies of disease clusters have strongly suggested asymptomatic transmission. Asymptomatic individuals who spread it to a bunch of family members despite having no symptoms, then tested positive for the disease themselves once identified.

There's no containing it at this point, the best you could do is slow it down until there's a vaccine.