  An adequate near-optimal control problem for a stochastic SICA
(Susceptible-Infected-Chronic-AIDS) compartmental epidemic model for HIV
transmission with imprecise parameters is formulated and investigated. We prove
some estimates for the state and co-state variables of the stochastic system.
The established inequalities are then used to prove a necessary and a
sufficient condition for near-optimal control with imprecise parameters. The
proofs involve several mathematical and stochastic tools, including the
Burkholder-Davis-Gundy inequality.
