The disease cycle of wheat stem rust starts with the exposure of each new wheat crop to spores of Puccinia graminis f. sp. tritici, which are the primary inoculum. The source of the first spores that infect the new wheat crop differs depending on the region in which the wheat is grown. Details can be accessed at:
"Stem rust (caused by the fungus Puccinia graminis) can only survive from one season to the next on a living host. It does not survive on stubble, seed or soil. The most important hosts are susceptible wheat, but it can also survive on barley, triticale and some grasses. Carry over on wheat from one season to the next is greatest during wet summer/autumns." [1]
"Leaf rust is caused by the fungus Puccinia triticina (formally Puccinia recondita). Leaf rust, like other cereal rusts, requires a living host to survive from one season to the next."
Wheat leaf rust spreads via airborne spores. Five types of spores are formed in the life cycle: Urediniospores, teliospores, and basidiospores develop on wheat plants and pycniospores and aeciospores develop on the alternate hosts. The germination process requires moisture, and works best at 100% humidity. https://en.m.wikipedia.org/wiki/Wheat_leaf_rust