Not at all. The spike in numbers was due to change in tracking the incorporates any signs of chest infection instead of waiting for confirmation of coronavirus. Prior to the spike in numbers, the tracking for newly infected looked like this:
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That's a pretty pronounced downward trend. We also see places like the quarantine at the Arrowe Point Hospital in the Wirral, UK, see zero cases out of 80 kept under observation. This strain of coronavirus doesn't appear to be particularly infectious compared to viruses in general. Certainly the UK health officials aren't treating it as a problem. A confirmed case was taken to hospital in an Uber, but the health officials haven't felt the need to quarantine the driver. Likewise where cases have been known, advice to those who came into contact with the infected is to carry on as normal unless you exhibit symptoms, in which case self-quarantine. That suggests it's not contagious during the incubation period, and not hugely contagious outside. The virus is also vulnerable to standard hygiene measures (disinfectants).
It's not a highly contagious air-born disease and so far looks less contagious than typical colds and flu. I think the real test case is the UK university. A confirmed case of a student living in close proximity to lots of other students - that'll show if coronavirus can spread quickly or not.