Count data with consecutive counts

[Mkkl]

Hi there,

I was wondering how to approach predicting the length an individual/observation is in a specific process.
Basically, I have a dataset which contains a positive number of days that an individual is in a process, which I am trying to predict.
This lead me fairly quick to modelling count data by means of a Poisson or Negative Binomial Regression, however, this only entails a number of times an event occurs within a specific time frame as far as I understand.

I also thought of approaching this problem as an ordinal classification problem or from a survival analysis perspective.

Does anyone have some thoughts on this subject?

Any help is appreciated!