In a nuclear reactor, a fissile substance, such as uranium or plutonium produces a fission chain reaction. In such substances, a few atoms fission from time to time, due to spontaneous fission or neutrons introduced from an outside source. When this happens, more neutrons are released. Each fission reaction releases more neutrons. Some of those neutrons strike other atoms and produce fission and some do not. In a small pile of uranium, a few fissions will happen, from time to time, and those fissions will sometimes cause more fissions to occur, but most neutrons will not produce more fission, so while one fission event may spawn a few more, it will not produce anything sustained.
You might expect that as the amount of fissile material increases, the amount of fissions would increase at a relatively linear rate to the amount of material. That, however, is not what happens. As more material is added, very little happens. Spontaneous fissions continue to occur, but the rate at which secondary fissions occur increases by a very modest amount. Then, at some point, it all changes, the relatively flat increase in fission rate suddenly surges, and within microseconds, the material has gone form a few isolated fission events to continuous sustained fission.
The reactor has reached what is known as “critical mass.” This is the point where each fission that occurs produces at least one more fission on average. It may go beyond being critical to becoming “super critical” where the rate of fission increases dramatically in a short period of time. Because critical mass is such a sudden tipping point, it can come without warning, as has been the case in criticality accidents. It’s also why a nuclear bomb can go from almost no fissions at all to fissioning nearly the entire mass of plutonium or uranium in nanoseconds.
What does this have to do with disease? More than one might think.
If an infected individual is introduced to a population of uninfected individuals, whether the disease will be able to grow to a full-blown outbreak has a great deal to do with what percent of the population is susceptible to that disease, for example, because they are not vaccinated. The exact number of persons without vaccination needed to sustain an outbreak depends on the nature of the disease, such as how easily it is passed on, how long it lasts and the method of transmission.
In general, if only a small number of persons are susceptible to the disease, the initial infected person may pass it onto one or more others and those others may or may not pass it on to one or more others, but the number of cases stemming from each infected individual is small enough that the disease never gets a real foothold in the population and never manages to infect more than a handful of persons before the outbreak fizzles out.
At some point, however, enough people are not vaccinated that each new infection has a pretty good chance of passing it onto someone else, thus sustaining the outbreak and resulting in numbers of infections that increase exponentially.
And that is how THIS happens:
The above graph is from the CDC and shows the number of cases of Pertussis (whooping cough) in Washington State, although similar graphs exist showing outbreaks elsewhere. Pertussis is a disease that causes fits of coughing and respiratory distress. In adults, it can be a miserable condition, but is rarely dangerous. In children, it may require hospitalization, and in infants, it can easily be deadly.
The reason for the outbreak boils down to the fact that more and more parents have been avoiding vaccinating their children because of bogus claims of vaccine dangers. This trend has been going since the 1990’s. Health officials had been warning of the dangers, but most saw few repercussions. Whooping cough rates have been going up, but only at a relatively slow rate.
Then, between 2011 and 2012, the number of cases increased by as much as 25-50 times! This graph gives a bit more context to how dramatic this spike is.
At this point, that threshold has been crossed. There is no longer enough herd immunity to prevent an outbreak. Critical mass has been reached. The outbreak is now self-sustaining and can grow and spread across the population. A single case no longer just triggers a handful more. Once one of these outbreaks starts, it’s very difficult to stop, at least until the level of vaccination has reached the point where the virus no longer can spread from host to host fast enough to sustain the epidemic.
Understanding the mathematics behind this is more than academic. It explains how a massive outbreak can creep up on the population. As the level of immunization drops, there may not be a dramatic increase in cases until it suddenly spikes.
This entry was posted on Saturday, September 8th, 2012 at 1:28 pm and is filed under Bad Science, Good Science, Nuclear, Quackery. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
View blog reactions