After you have wart-free for at least 3-6 months, then you can consider yourself not infectious at that time. What you don't know is if you will be infectious 5-10 years from now. No one knows this but the odds are good you won't be.
Your highest priority now is your good health. Refrain from sex until they are gone for good. Have your partners use a condom always. Informing future partners is up to you. Understand that nearly everyone has it if they have been sexually active. If you smoke cigs or lead an unhealthy life, then use this moment to change. Your sex life will recover as it did for everyone on this site.