+ Translate

Epidemiological studies on catastrophe theory

, : Epidemiological studies on catastrophe theory. Bulletin of Azabu University Veterinary Medicine 2(2): 243-256

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.

(PDF 0-2 workdays service)

Accession: 005375452

Submit PDF Full Text: Here

Submit PDF Full Text

No spam - Every submission is manually reviewed

Due to poor quality, we do not accept files from Researchgate

Submitted PDF Full Texts will always be free for everyone
(We only charge for PDFs that we need to acquire)

Select a PDF file:

Related references

Loehle C., 1989: Catastrophe theory in ecology a critical review and an example of the butterfly catastrophe. Catastrophe theory is no longer new but it remains controversial. Controversy arises not out of the mathematical foundations of the theory nor from applications in the hard sciences, but principally when it is applied to the social and biological...

Nishizawa, K., 1976: Dynamic theory on hemolysis of the X-ray irradiated erythrocytes based on the catastrophe theory. Nihon Igaku Hoshasen Gakkai Zasshi. Nippon Acta Radiologica 36(7): 631-635

Theocaris, P.S.; Michopoulos, J.G., 1982: Generalization of the theory of far-field caustics by the catastrophe theory. To generalize the theory of far-field caustics, three theorems and several corollaries are presented in this paper. Using the law of reflection and catastrophe theory we have established conditions to predict caustic patterns in a 3-D space, which...

Senechal, M., 1977: Catastrophe theory. Science 196(4296): 1270-1270

Deakin, M.A., 1977: Catastrophe theory. Science 196(4296): 1272-1272

Lewis, M., 1977: Catastrophe theory. Science 196(4296): 1270-1270

Neskovic; Perovic, 1987: Ion channeling and catastrophe theory. Physical Review Letters 59(3): 308-310

Zeeman, Christopher., 1992: Evolution and catastrophe theory. Unknown

Nye J.F., 1987: Catastrophe theory in geophysics. NATO ASI Series Series C: Mathematical and Physical Sciences

Sussmann, H.J., 1977: Catastrophe theory: a skeptic. Science 197(4306): 820-821