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.Comment: This is a preprint of a paper whose final and definite form is with
'Applied Mathematics Letters', ISSN 0893-9659. Submitted 22/Jan/2018; Revised
03/May/2018; Accepted for publication 03/May/201
