HPV reinfection after tx

I had a leep procedure done 3 years ago for cervical cancer and had negative paps ever since.  Does this mean I am in a "latency" period now?  How does this affect the rate of infecting a partner or passing on the virus?  If you get rid of the abnormal cells does it decrease the possibility of infecting others or is the virus still as easy to "catch"?  I'm unclear of where this virus lives- in your cells on the cervix? in your blood stream? When you say you pass it from skin to skin transmission- do you have to have a current infection or abnormal skin cells in order to "pass it on"?