It seems to be common practice to ignore the nominal welded wire ladder reinforcing ("Brickforce"

used in brick bed joints. The South African code for unreinforced masonary (SABS 0164-1) makes no adjustment to the flexural strength of masonary to allow for reinforcement. The other code for reinforced masonary only makes reference to types of steel bars and prestressing like those used for reinforcing of concrete.
The control of placement accuracy and adequate bond would be a concern if the welded wire reinforcement were to be considered structural to provide flexural strength in masonary. There are also concerns that the wire, even if galvanised, does not have a very long life in outside walls in wet climates (Botswana is excluded here) before corrosion begins.
In the case of single-leaf walls (half-brick thickness in British terminology) the thin wire cross-sectional area and small eccentricity from the centroid of bending would only make a small contribution to the overall stability, particularly if strong arch action is developing in the masonary.
If you were to do the calculation ignoring arch action, you would probably also find that the wire reinforcement would contribute an insignificant amount to the stiffness and servicibility limit state of the wall, although I agree with suggestions that it could contribute usefully to the ultimate (collapse) limit state.
I have always used normal reinforcing bars (Y8 etc) rather than welded wire in the bed joints where reinforced lintels etc are required.