White noise

Quantum mechanics

Epidemic model

Biology

Stochastic partial differential equation

Statistics

Geomorphology

Differential equation

Stochastic process

Applied mathematics

Virology

Extinction (optical mineralogy)

Perturbation (astronomy)

Stochastic differential equation

Telecommunications

Sound (geography)

Computer science

Mathematical optimization

Acoustics

Environmental health

Statistical physics

Geology

Stochastic modelling

Paleontology

Environmental noise

Physics

Mathematics

Optics

Human immunodeficiency virus (HIV)

Population

Mathematical analysis

Ordinary differential equation

Uniqueness

Medicine

Transmission (telecommunications)

Partial differential equation

Applied Mathematics Letters

We propose a stochastic SICA epidemic model for HIV transmission, described by stochastic ordinary differential equations, and discuss its perturbation by environmental white noise. Existence and uniqueness of the global positive solution to the stochastic HIV system is proven, and conditions under which extinction and persistence in mean hold, are given. The theoretical results are illustrated via numerical simulations.

A stochastic SICA epidemic model for HIV transmission