Smilax and rust

Smilax (Asparagus asparagoides) is one of the 10 worst weeds in NZ.
Smilax rust (Puccinia mysiphylli) infects Asparagus asparagoides, like this:
http://m.nzpcn.org.nz/flora_images_large/Asparagus-asparagoides-06e.jpg

My neighbours and I used to have large banks of Smilax, then it became affected by the rust and mostly died.
Now I have half a dozen new growths of Smilax. I have obtained some Smilax rust and taped it to all the growths. Only one has died after a week.
I expected that the rust would immediately affect the Smilax.
Does anyone know more than I do? (probably not!)
I am trying to get rid of all Smilax in my neighbourhood.

AFAIK the rust isn't instant death, it sickens the plant and limits seed set. Australian trials talk of the rust taking 5-10 years to get control of an area, the important thing being getting the rust widely established.

Thanks. I imagine the rust is spread by the wind. I thought that taping some infected Smilax directly to each plant would infect that plant.
I have killed most of it by spraying several times with Glyphosate.
Digging out the roots is almost impossible as a tiny plant has half a rubbish bin of roots.

One plant seems to have now caught the rust and another plant has died completely. I am monitoring two more plants.