On Feb. 24, 2009, NOVA ran a special on the mautaam event in India: http://www.pbs.org/wgbh/nova/rats
Apparently, once every 48 years, the bamboo flowers and produces an enormous quantity of fruit, which in turn causes a population explosion among the black rats in the forest. Once the fruit is gone, this plague of rats devours the rice fields, causing a lot of human suffering.
The math is simple: exponential population growth. What is staggering is the sheer rapidity of rat reproduction when there's no limit to the environmental carrying capacity. This is a great, real example to use with your students of exponential growth.
Here are the details I looked up: black rats have a gestation period of 21 days and can have a litter of about 10 pups at a time; female rats can nurse a litter while also pregnant; and rats reach sexual maturity in 6 weeks and therefore can have their first litter at 9 weeks of age. These facts produce explosive -- yes, explosive -- population growth. You can model the growth by tracking the size of each age cohort (newborns, adolescents, mature adults) in a spreadsheet, like I did in this one:
Or, you can model the growth with a recursive formula:where a is the time in weeks. You can also come close with an explicit formula,where t is the time in weeks. I graphed this explicit formula into the spreadsheet as well. The upshot is that the rat population comes close to doubling every three weeks; in the four month season of mautaam, the population grows nearly 120-fold. That's a real plague of rats.