In that case you could connect the currentIndexChanged signal to a slot in your GUI class, convert the QString to an int and call the method from your application class. Of course, instead of calling the method directly you could also define and emit a custom signal which you connect to the slot from your application class. You can find an example in the Qt documentation.
The question is, why don't you want any Qt code in your application class? If that class has a slot, you have Qt code already in there.
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