If you're familiar with FFMPEG, there are a few solutions out there to capture the screen via that tool, here is one way.
Then it is just a matter of taking that resulting command and blending it with output to an mpeg-ts stream to Wowza Streaming Engine.
This article shows how use ffmpeg to send different inputs to Wowza as MPEG-TS.
Similar can be done with VLC as well. Here's an article on how to send streams to Wowza using the VLC command line.
The input half of the command is somewhat easier than FFMPEG though:
vlc -vvv screen:// :screen-fps=24