For me, "Italy" sounds convincing, because it is closer to us -- I live in Europe --, geographically and culturally, than China. (Talking about China feels about as relevant as talking about Mars.)
A video from Italy, showing the crowded hospitals and soldiers on streets, would probably feel more convincing than citing numbers. (Also, this was shared on SSC.) I would only cite numbers afterwards to say something like "see, two or three weeks ago they also had only X known cases".
I would probably try convincing along the lines of: (1) if everyone will stop their social life in two weeks anyway, we might as well do it today, and (2) many people are asymptomatic or have mild symptoms, and the incubation time is several days while people already spread the virus, so by the time you know 1 person in your neighborhood to have severe symptoms, there are probably already hundred who spread the virus.
Also, when talking about the probability of death, I would add that even "non-death" can mean a lot of pain and irreversibly damaged health.
Most people are altruistic, therefore I would emphasise "you might unknowingly infect people you care about" over "you might get sick and die". (Also, gender stereotypes: men are socially conditioned to not worry about what happens to them, but they are supposed to protect their families.)
If your parents don't have Skype (or equivalent) ready, install it now.
Start buying stuff for your parents even before you have convinced them. Say "I know you don't share my worries, but knowing that you have this stuff makes me feel much better, please accept it".
If she manages to convince them later, the supplies will already be there, so it's definitely a good move.