The virus that causes COVID-19, SARS-CoV-2, is phylogenetically most closely related to SARS-CoV, the virus that causes SARS- this is why taxonomists named it SARS-CoV-2.
However, you shouldn't and can't expect SARS-CoV and SARS-CoV-2 to have a more similar course because of this, as compared to MERS-CoV- and in fact thus far they've behaved differently. For instance, the death rate for COVID-19 is considerably lower than for SARS. Paradoxically, this may be responsible for its greater spread, because people who are less severely ill or asymptomatic are much more able to spread disease widely or in an undetected fashion. In the US there has been undetected community spread of SARS-CoV-2.
I don't think it's useful to use epidemiological properties of other related strains at present; the data we have directly about SARS-CoV-2 is already superior to extrapolating this way. COVID-19 has already expanded far more geographically than SARS ever did, which already makes the overall probability of extinction of it less likely than with SARS, as generally speaking extinction probability decreases with increasing population size.
Marielle has covered SARS and COVID-19 well. Both of these viruses leaped from animals to humans exactly once and then spread human-to-human. It's believed that the MERS virus exists in the camel population and leaps to humans many times, with human-to-human transmission then occurring from each of those introductions. But it does not spread nearly as well as either of the other ones, and is the deadliest of the 3. This is probably not a coincidence.
I'll comment here but first thanks to both Marielle and CellBioGuy.
Just as informational input I am curious if we have good understanding (meaning once we see a virus we can predict) of why some viruses would more easily make the jump repeatedly while others are perhaps highly unlikely mutations?
Also, more at CellBioGuy, have you seen any of the stories suggesting the outbreak in the Wuhan market was actually human-to-human and not wild-to-human? If it were the case that the COVID-19 outbreak really was not a jump from an infected animal to a human wo...
Can anyone explain the difference (lay terms) between the coronavirus strain that produced SARS and the one the produced MERS?
On reason I ask is that SARS seems to have died out (last reported case in 2004). However MERS is still being reported periodically.
Would knowing these differences, and with what is currently known about COVID-19, can something be said about COVID-19 and expectations of how it plays out over time? Could we expect it to die out like SARS, be semi controlled but still infecting people over time?