There are 118 types of HPV, amongst them 40 are infecting genital tract and 12 are known to cause cancer. From the 12 only 8 cause most of HPV related cancer. They are -- types 16, 18, 45, 33, 31, 52, 58, and 35 in descending order of frequency and are responsible for more than 90 percent of cases.
Recently vaccines against HPV have been developed, those cover types 16 and 18 fully; and types- 45 and 31 partially. With the present knowledge multivalent vaccines need to be developed.
The problem is that the HPV vaccine is costly and most of the times inaccessible to poor who are predominantly affected. Probably states need to support development of multivalent vaccine.