Catastrophe theory is the mathematical theory that explains the observation that small incremental changes in the value of a variable in a natural system can lead to sudden large changes in the state of the system. The best-known, everyday example is the change in the state of the chemical H2O from solid (ice) to liquid (water) to gas (steam). The same processes occur in nature with many other chemical substances. In biology, medical practice, and public health there are many examples of catastrophe theory in operation. They include certain stages in the process of carcinogenesis and spread of cancer, in gene frequencies in populations, and in phases in the development, continuation, and decline and disappearance of epidemics. The same processes operate in the dissemination of ideas, innovations, and fashions.
The word "catastrophe," with its suggestion that the outcome is always undesirable, may have been an unhappy choice to describe this process. While this is certainly the case in the explosive onset of many epidemics, the same mathematical process operates in reverse when an epidemic or epidemic disease virtually disappears quite suddenly from a population. This happens when the balance of susceptible and immune individuals shifts from the proportion required to sustain an epidemic to a marginally smaller proportion where the probability of transmission of an infectious agent to a susceptible host falls below the critical level required to sustain the epidemic. Catastrophe theory should not be confused with chaos theory, although both may operate together in some circumstances.
JOHN M. LAST
(SEE ALSO: Chaos Theory; Epidemic Theory: Herd Immunity)