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There was no outbreak of small pox. Hasn't been one case for more than 20 years.

If you know of a case, please contact the World Health Organization.

Bill Shaeffer has written several papers on measels in baltimore. Baltimore has records of epidemics going back about 200 years. He has a differential equation model that works pretty well, and categorizes folks as immune, not exposed, and active. Basically it is a nonlinear differential equation, and the immune population acts as a damper.

There are two kinds of vaccine- live vaccine which gives people a hopefully benign form of disease, and killed vaccine which exposes people to the killed fragments of the most virulent form of the disease. Sabin is one, Salk is the other. The problem with Sabin-live vaccine is the potential to mutate to another more virulent form. The problem with Salk-killed vaccine is the potential that the virus is not completely killed.

In the long term, the population level problem is the potential for disease associated with a vaccine, (from mistakes, non-killed agent, mutation of live agent, or allergy from the growth medium). Because of that risk, once the disease incidence is low enough, it makes short term sense to not give anyone vaccine. That allows the non-immune population to build up, and the stage is set for an epidemic. Take smallpox now. It is no longer routine to get immunized for smallpox. Because of that, the immune population is no longer damping the rate of growth. A single case (perhaps caused by exhuming a 100 year old corpse) and the disease would take off like wildfire!

by comparison, a constant low level of disease (say 5 percent) would tend to have the more benign form (because it limits the ability to pass on a disease, if the host is killed) yet a moderate vaccination level could be sustatined since the risk of the vaccine would always be less than that of the disease when unvaccinated.

Illusion that small pox has gone away. No cases for 20 years provides that illusion. Yet the virus still sits and waits in the ground, waiting for a chance. Our public health policy, since it seeks to recommend actions to provide the lowest risk NOW, sets us up for an epidemic in the future. One can optimize for X or optimize for X' (the derivitive of X) but they are different things, and different paths will get different results.