Capacity planning is one of them.

I have used first order differential equations to model the user adoption growth on Internet transactions. From there you can derive concurrent users of the system and based on the hardware/software specifications give the amount of servers/bandwidth needed.

This also serves to model your software behavior and its impact on the capacity plan(e.g. if you have inefficient code that needs to be redone due to its running complexity because you have only N servers or x response time as constraint based on the growth model).

You can see this discussion

https://www.google.com/amp/s/www.researchgate.net/post/Applications_of_computer_science_and_computer_engineering_uses_partial_differential_equations/amp