Changes in the virulence of the SARS-CoV-2 will be driven by evolutionary pressure. We know so far that the virus is mutating slowly
The COVID-19 virus does not mutate very fast. It does so eight to 10 times more slowly than the influenza virus, said Anderson, making its evolution rate similar to other coronaviruses such as Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS).
but there is currently no evolutionary pressure to select out any one strain over another because they are so similar
The virus mutates so slowly that the virus strains are fundamentally very similar to each other,” said Charles Chiu, a professor of medicine and infectious disease at the University of California, San Francisco School of Medicine.
For a virus to mutate to become more lethal does not make evolutionary sense. If it kills its host faster than currently, which would imply a shorter incubation period due to a higher replication rate, then it will reduce its ability to spread which is counter to evolutionary survival.
In fact we have data from a highly lethal rabbit virus that was accidentally released into the wild in Australia. It was almost 100% lethal but eventually the virus mutated to a less virulent form presumably because it had been killing too many of its hosts
The work showed that the almost invariably lethal progenitor virus strain was replaced within a few years by strains with case fatality rates of 70 percent to 95 percent. Some field isolates killed fewer than half the lab rabbits. Over the next few decades, things settled down, and strains at both ends of the lethality spectrum become increasingly difficult to find. Fenner showed why. The highly lethal progenitor virus killed rabbits so fast that its infectious period was shorter than that of the less lethal viral mutants. That meant that the less lethal strains were able to infect more new victims and spread throughout the population.
The rabbits also became more immune to the virus because again of evolutionary pressure and the virus mutated to overcome this resistance. But, we are not seeing any evolutionary pressure on account of SARS-CoV-2 because it's mainly decimating the older population who are past their reproductive lives.
The only evolutionary pressure on the virus I can imagine is if by widespread testing of more symptomatic individuals one might be taking out the more virulent strains letting a less virulent strain to persist in the population. However, the virus's slow mutation rate may prevent that.
Mutation data is being uploaded to a website called NextStrain.org that shows how the virus is migrating and splitting into similar but new subtypes.