White noise

Quantum mechanics

Chaotic

Hepatitis B virus

Biology

Statistics

Applied mathematics

Stationary distribution

Virology

Extinction (optical mineralogy)

Markov chain

Telecommunications

Sound (geography)

Computer science

Acoustics

Statistical physics

Stochastic modelling

Paleontology

Hepatitis B

Environmental noise

Physics

Nonlinear system

Mathematics

Optics

Image (mathematics)

Lyapunov exponent

Econometrics

Lyapunov function

Mathematical analysis

Artificial intelligence

Medicine

Transmission (telecommunications)

Virus

Noise (video)

Ergodic theory

Chaos Solitons & Fractals

Environmental factors such as, humidity and temperature pose significant impacts on the dynamics of hepatitis B virus (HBV). The stochastic modeling has been proved to be a powerful tool for revealing such impacts. With this motive, the present study enacts the formulation and analysis of a stochastic hepatitis B model considering a time-delay in the transmission coefficient, and CTL immune response class. Initially, the model is investigated for the existence of a unique global solution. By using the stochastic Lyapunov functional theory, the model was further analyzed for extinction and persistence of the disease. It is evident that the ergodic stationary distribution exists under certain condition. We infer that the white noise plays a significant role in controlling the infection. Relatively large noise guarantees the extinction of HBV. Similarly, it is inferred that the delay factor is responsible for the periodic occurrence and re-infection of the disease. Additionally, for providing a strong support to the theoretical results, sample trajectories were displayed at the end of the study.

Delayed hepatitis B epidemic model with stochastic analysis