Dear friveroll

Maybe it is annoying but before modeling data you have to define your goals. I am not a biologist but developed a large amount of models in the last years together with biologist, pharmacologist,… . You have to clearly state what you actually want:

If you just want to describe the data by a mathematical model with a slight biological background I could help you. But as I said before if you want to physiologically interpret the model parameters such a model will not really help. So the main question is, for what you will use the model (pharmacological parameter interpretation, simulation,..)

If you are also interested in drug response on the target (I am still not sure if or if not), then you have to apply the concept of pharmacokinetic / pharmacodynamics modeling. This is the standard concept in pharmacological modeling in industry and academics. If I understand you right there is an influence of a drug on your data. So without taking the drug into account in your model every model will be worthless. Note that PKPD tries to mimic the underlying biological mechanism and as a result they describe the data. The models are not developed with just looking at the data. Therefore, you cannot just take a model from literature to apply it to your situation.

I would like to help you but to get a better overview please answer the following questions

Are you familiar with PKPD?

Do you know what differential equations are?

Did you ever develop a mathematical model?

Which mathematical models you already applied?

Which software do you use?

What is your background (PhD….)