Quantum mechanics

Epidemic model

Demography

Mathematical physics

Biology

Statistics

Stochastic process

Applied mathematics

Stationary distribution

Virology

Degenerate energy levels

Markov chain

Computer science

Environmental health

Statistical physics

Exponential growth

Thermodynamics

Physics

Diffusion

Database

Mathematics

Human immunodeficiency virus (HIV)

Invariant (physics)

Population

Sociology

Mathematical analysis

Measure (data warehouse)

Medicine

Invariant measure

Ergodic theory

Applied Mathematics and Computation

This paper studies a stochastic HIV-1 infection model with degenerate diffusion. The asymptotic dynamics of the stochastic model are shown to be governed by a threshold parameter. When the parameter is negative, the infection is predicted to go extinct exponentially while the level of healthy cells converges weakly to a unique invariant measure. When the threshold parameter is positive, the solution of the stochastic model converges polynomially to a unique invariant probability measure, indicating that the system admits a unique ergodic stationary distribution. Numerical simulations are conducted to show the analytical results. These results highlight the role of environmental noise in the spread of HIV-1. The method can also be applied to the non-degenerate systems.

Analysis of a stochastic HIV-1 infection model with degenerate diffusion