Data from human clinical trials have shown that the hepatitis B virus (HBV) follows complex profiles, such as bi-phasic, tri-phasic, stepwise decay and rebound. We utilized a deterministic model of HBV kinetics following antiviral therapy to uncover the mechanistic interactions behind HBV dynamics. Analytical investigation of the model was used to separate the parameter space describing virus decay and rebound. Monte Carlo sampling of the parameter space was used to determine the virological, pharmacological and immunological factors that separate the bi-phasic and tri-phasic virus profiles. We found that the level of liver infection at the start of therapy best separates the decay patterns. Moreover, drug efficacy, ratio between division of uninfected and infected cells, and the strength of cytotoxic immune response are important in assessing the amount of liver damage experienced over time and in quantifying the duration of therapy leading to virus resolution in each of the observed profiles.