How long after a URI is a cat typically contagious and if both cats have had it at one point do I ne

Hello all! If my cat is still sneezing, does that mean he still can spread a URI?  We adopted a shelter cat who gave a URI to my current cat Pete.   It has now been 3 weeks today that Pete first came down with it.  He has done his antibiotic treatment and is pretty much normal, minus the sneezing.   The cat that gave it to him, our new shelter cat started showing symptoms about 5 days before my cat Pete.  The new cat Jinx is at my moms house, he is not sneezing at all.  

So I guess my question is can I put these two cats together at this point.  If they have both have it, does it matter…and if one cat is sneezing does that mean he is still contagious?  

Uhgg, this is so confusing. 

Sneezing and Feline Upper Respiratory Disease

http://www.peteducation.com/article.cfm?c=1+2134&aid=210

Most likely they are neither contagious.  Since they've both been on antibiotics you can start introducing them if you haven't done that already.