What does prom mean in these sentence?

prone means that the thing is more likely to happen to the person or thing than for most people.  It means the risk is very high for the person who is prone.  Something about the person or thing makes such events happen a lot more than is usual for the general person or thing.

"prom" ought to be replaced by "prone" which is an adjective meaning likely to suffer from something or to do something bad.
After "prone" "to" is generally used.Also, after "prone""to" is used.

Working relentlessly makes us more prone to error.
Tired students were found to be particularly prone to ignore basic academic rules.
Synonymous-prostrate.

It means almost the same as 'susceptible' or 'vulnerable'.

Read the sentence and your question carefully! The word is 'prone' not 'prom'. Being prone to a named type of medical problem means that the problem is likely to occur to that person, probably several times.