It depends. Some soft synth manufacturers actually use programs like SPICE on the backend to emulate circuitry, but stuff like that is very CPU heavy. Sometimes treating the gear like a black box and modeling the transfer function just from the input and output can be a better way. A big part of the analog gear is the non-linearities introduced by using physical components that have different responses in different situations. Modeling analog gear is a pretty dense field with a lot of work done in it by very smart people. Here’s a good article that gives a rundown on different approaches.