is there a mathematical model of hepatitis viral b?which is it?

There was, and continues to be, a lot of work on mathematical modelling of various aspects of viral infection and spread.

This started apparently with the work of Daniell Bernoulli on smallpox in 1760, and continues to this day. A special 5 year effort on mathematical modelling of viruses by DIMACS is described in one of the references below. There is probably a lot of material associated with mathematical modeling of viruses that one could find in connection with this DIMACS effort.

I also include a reference to a book that describes some mathematical modelling of the hepatitis B virus, and some other references.