The compartmental analysis figure is the diagram that I want to translate to differential equations and eventually analog computer.

This is from

This book. IDK about the author, but I bet that this is extremely reliable compared to the materials locally available and written by local authors. But it doesn't tell which equation it is modeling, so I am not 100% sure about it.

It has problems as well-:

It doesn't use negative for K12 And idk why is it using negative for K23.

Less reputed source-:

This is pretty ambiguous, their equation and figure don't even match.

Highly reputed source(LOCAL)-:

My thoughts about sign what they should be-:

If the arrows are coming towards the block in consideration, add + sign else add - sign.

For eg-: consider x1 block, then we find x1', for that + will be what comes inside i.e K21*x2, and - will be what goes outside ie.K12*x1.

My Teacher(He hasn't written any pdfs that I know of)-:

He says "some books have written plus(in K21) while some minus I am not sure what it is actually."