I think a lot of people here will equate software/programming to mathematically modeling.
Saying you can model/math it, but not use software analogies, is just really trying to split hairs, since models/math is also software.
At any rate digital (0,1) strings aren't that different than DNA strings (A, T, C, G) and just because we have 4 characters in the alphabet doesn't mean you can't analyze it as an abstract computational process.
You can also discretize the concentration of molecules such that above a threshold switch like behavior occurs (gene turns on or off).
Also people have done experiments where they program DNA to perform computations to solve various problems like the traveling salesman problem. This is a direct application of using biology to solve a "digital problem" https://www.nature.com/articles/news000113-10
So here we have an example of an artificial logical problem encoded into DNA and solved using biology. That means biology can simulate computational algorithms.
Of course you can model various aspects of cells mathematically. But that doesn't require any analogies to software.