Stochastic Simulation of Hepatitis B Virus Infection: Modeling the Viral Persistence and Clearance of the Environmental Noise

Résumé

Hepatitis B virus (HBV) infection has remained an important health concern in the world with its
dynamics being complex with deterministic biological processes as well as stochastic
environmental changes. This study formulates and examines a holistic stochastic differential
equation (SDE)-based model to establish how environmental noise influences the dynamics of
viral persistence and clearance. Building on the classical deterministic HBV model whereby the
multiplicative noise terms are added to account for the random variation of viral replication, human
immunity and cell dynamics. Deriving the conditions under which the disease will be eliminated
or remain, using intensive mathematical analysis and widespread numerical simulations, in terms
of a stochastic basic reproduction number ð‘…0
ð‘ . The intensity of environmental noises can be
important in influencing the likelihood of viral clearance and intermediate levels of noise may
enhance clearance where deterministic models would persist with clearance is shown. Obtaining
explicit formulas of the stationary distributions, investigate the average time to extinction, and
measure the dependence of the noise parameters and clinical outcomes. This model is tested on
longitudinal HBV DNA data of chronic carriers of hepatitis B who demonstrate great consistency
between the simulated trajectories and clinical observations of HBV DNA. The stochastic effects
cannot be overlooked in HBV modeling and give theoretical justification to the use of treatment
strategies that utilize the variability of the environment to improve viral clearance.