How to put different business logic together?

I'm trying to design a model to put many different business logic together.

For example , there are some red point(I don't know the exact words) in app (android or ios and so on) to indicate some messages which need user to read . Each red point has its own logic , and some red points' logic will be effected by others. So the code will be very complex.

So I'm wondering is there a design pattern (or other ways) could put those red points' logic together, if I write the logic everywhere, it will be very difficult to maintain.