How to build cycle graphical model with inference

Hi Everyone

First, thank you very much for taking the time to help. Your help and time will surely be appreciated.

I have a question about of probabilistic graphical models. Please check this pdf file https://drive.google.com/file/d/1LytPwN0EHKSn8jJvLWfpIKpBZ63Liwo7/view?usp=sharing . It explains the model that I need to build. It also presents the inputs the model should process as well as the output required.  

Can you kindly have a look at this file, and suggest me the best way to build such a model?    

Thank you again.