A generalized distributed delay model for HBV infection with two modes
of transmission and adaptive immunity: A mathematical study
Abstract
In this paper, we formulate a generalized hepatitis B virus (HBV)
infection model with two modes of infection transmission and adaptive
immunity, and investigate its dynamical properties. Both the
virus-to-cell and cell-to-cell infection transmissions are modeled by
general functions which satisfy some biologically motivated assumptions.
Furthermore, the model incorporates three distributed time delays for
the production of active infected hepatocytes, mature capsids and
virions. The well-posedness of the proposed model is established by
showing the non-negativity and boundedness of solu- tions. Five
equilibria of the model are identified in terms of five threshold
parameters R0, R1, R2, R3 and R4. Further, the global stability analysis
of each equilibrium under certain conditions is carried out by employing
suitable Lyapunov function and LaSalle’s invariance principle. Finally,
we present an example with numerical simulations to il- lustrate the
applicability of our study. Nonetheless, the results obtained in this
study are valid for a wide class of HBV infection models.