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Tanizawa S.

1981

Bulletin of Azabu University Veterinary Medicine 2(2): 243-256

Epidemiological studies on catastrophe theory

A dynamic system was constructed in the space of the epidemic of a contagious disease (epidemiological space) and the catastrophe theory was introduced to express the actual mode of the epidemic of a contagious disease (influenza, 1959) as a movement of the potential (disease intensity). The following conclusions were drawn. In the partial control space Rk of the epidemiological space, the primary, secondary and tertiary movements obtained from the curve of the number of patients appearing each day vs. the time were adopted as a basis. The model of the epidemic of a contagious disease was constructed as a dynamic system Rk .times. R1 .fwdarw. R, where k = 1, 2, 3 or 4 dimensions. The primary and secondary moments were selected as the basis of the control space to study the epidemiological significance of a cusp model. By adding the tertiary moment to this, the swallow tail model was studied. By further adding time as the 4th control factor, the butterfly model was studied. The primary and secondary moments (normal and splits factors in the catastrophe theory), the tertiary moment (as the bias factor) and the time (as the butterfly factor) were judged to be of epidemiological importance. The butterfly model containing the cusp and the swallowtail model is expected to be the most adequate model for the dynamic eludication of the epidemic of a contagious disease.
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