The World Health Organization states that a Yellow Fever vaccination is effective for 30-35 years, possibly for life. So you don't need to be re-vaccinated.
To enter Saudi Arabia you will need your Yellow Fever Vaccination card.
In December 2007 the WHO adopted a new-style of YF Vaccination certificate, however the old style (which you'll have) is still valid for 10 years from the date of issue.
As for meningitis: there are several types of meningitis. Not sure which one you're talking about. Have a look at the FAQ on the CDC website here:
and get some advice from your doctor about what's appropriate for you (make sure you go to the doctor 6 to 8 weeks before departure). Phil about 10 years ago