According to the reading, it seems like a vaccine that includes multiple HPV strains should include HPVs 16, 18, 31, and 45 at minimum. This would stem the root of a reported 80% of cervical cancer associated HPV infections. This is the ideal likely gives the best cost/benefit analysis, but it does leave the window open for other carcinogenic HPV strains to take hold and increase the proportion of cancers that they cause.
If we wanted to most effectively eliminate cervical cancers associated with HPV, we would include all of the other associated carcinogenic HPV strains (HPVs 33, 35, 39, 51 52, 56, 58, and 59). This would, however, be extraordinarily expensive to develop, produce, and (due to the nature of healthcare in America) administer. Likely so expensive that nobody would willingly sink the costs to produce a vaccine with every carcinogenic HPV strain, and very few people would go about getting it.
One possibility is that the most carcinogenic HPV strains could remain separated as different vaccines as opposed to mixed into one. This might make it more cost effective and more people might be inclined to get at least one of the shots. One potential issue with this set up would be needle phobias impacting rates of vaccinations.
The best time to administer these vaccines is before sexual contact, where HPV runs the risk of spreading. this can occur at any point, but likely before puberty would be a good starting point for vaccine doses.
Interestingly, after further research, it looks like a broad spectrum HPV vaccine is already being produced. Gardasil-9, a vaccine that protects against 7 of the most common carcinogenic HPV strains and 2 strains associated with genital warts, is already approved by the FDA and is being administered starting from the age of 9. This approval came mere weeks ago, after an accelerated FDA approval process that went through on June 12th, 2020.
