99.

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		2.5.2— Example of the Fractal Dimension of the Phase Space Set: Epidemics

		There is considerable variation each year in the number of people who get sick with communicable diseases such as measles and chickenpox. Are these variations due to chance, or are they due to the deterministic characteristics of how these diseases are transmitted from person to person?

		Olsen and Schaffer constructed the phase space set from the number of cases reported in time of different diseases in different cities. They found that the fractal dimension of the phase space set depended on the type of the disease and on the size of the city.

		The fractal dimension of the phase space set for measles was low. Thus the variations in the number of people with measles was mostly due to a deterministic mechanism. That is, the variations arise from the values associated with the rate of the transmission of the disease from one person to another, the duration of the incubation period before an infected person can transmit the disease, and the duration of the infectious period during which an infected person can transmit the disease.

		The fractal dimension of the phase space set for chickenpox was higher than that for measles. The highest fractal dimension that can be found from the phase space set is limited by the amount of data. Given the amount of data that they analyzed, they concluded that the fractal dimension of the phase space set for chickenpox was probably very large. This would mean that the variations in the number of people with chickenpox was due mostly to a random mechanism.

 

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