The infectious diseases can be classified by the pathogen: virus and bacteria (and prions?). We have vaccines for a few of them, it’s an important subset because they caused many dead. Vaccines are very specific, each one is against only one illness, or even only against some strains of the pathogens. (It’s possible to combine some of them to reduce the number of independent shots.)

We have eradicated smallpox! And I hope we will eradicate polio in my lifetime. There are many generic antibiotics against a lot of bacteria, and recently appeared some antiviral drugs. But the eradication or cure of all the infectious diseases is still a very long term objective.

The treatment for cancer has improved a lot. It’s a more difficult statistic that simply counting the number of dead, but it’s a hope. Also the tools for diagnosis have improved a lot, and that reduces the rate of false negatives and false positives, for example MRI.

Some cancers are clearly linked to virus. The most well known case is the cervical cancer (and a few similar cancers in other parts of the body). It’s (mostly) caused by the Human papillomavirus. There is a recent vaccine against the HPV, and it’s beginning to be applied massively. So I hope that in 50 years the number of cervical cancers will have lowered an almost disappear, but there will be still cervical cancer dew to radiation, chemical mutations, and other causes. There are other cancers that probably have a viral origin, and perhaps it’s possible to create a vaccine and eradicate them.

It’s possible to eliminate or cure some types of cancer, but a complete solution is almost impossible.