In the current work, we study the temporal dynamics of hepatitis B keeping in view the various routes of transmission and infectious periods. We develop the epidemic model to study its qualitative analysis, while keeping in view the asymptomatic and symptomatic infections periods. We then discuss the well-posedness of the proposed epidemic problem. Particularly, we show the boundedness and positivity as well as existence of solution to the proposed epidemic problem. We also calculate the basic reproductive number and discuss the local and global dynamical properties of the considered model. For the local stability, we use the linear stability approach, while for global stability the well-known LaSalle’s principle is used. Finally, all the theoretical parts have been supported with the help of graphical representation.