Yes, I'm aware the death note isn't real but it's interesting to talk about

In the rules of the show, the death note can be used to kill people by writing their name. The writer can also dictate how they want the person to die. There are limits, for instance, it can't be physically impossible.

So I'm wondering, could the death note user write that a person catches a deadly communicable disease and spreads it to five other people before they die. Then would the virus continue spreading and killing more people the user didn't directly kill with the death note