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The discipline of genetic epidemiology pertains to the vertical
transmission of the susceptibility (predisposition) to a complex
disease in a structured population. This statement meets halfway 1
the broad definitiongiven by N. E. Morton and S. c. Chung in 1978 2
and the concise one given by M. -C. King et al. in 1984. 1t
pinpoints the fundamental genetic hypothesis, namely, the existence
of an inherited condition that predisposes an individual to a
specific disease, and the corresponding subject ofinvestigation,
the family. Thus, the genetic epidemiological situation consists of
three basic elements: (l) the genealogical structure, (2) the mode
of inherit ance (i. e., the "genetic model") for the trait of
interest, and (3) the observable phenotypes of susceptibility. It
is clear that genetic epidemiology is a research field posi tioned
at the intersection of molecular genetics, population gen etics,
and clinical genetics. Perhaps the genealogical tree should be its
central element: it evidences something forgotten in mole cular
genetics, namely the relationships, and associations with
probabilistic and statistical concepts from population genetics. It
offers a structure and a "history" for those clinicians studying
familial diseases who are searching for genetic determinants of
susceptibility. The genetic epidemiologist begins his analysis with
a point on this genealogical tree, namely the proband, and attempts
to carry out (nonrandom) "ascertainment sampling" by using a
strategy that depends on the form and dimension (extended pedigrees
versus nuclear families) of the tree."
Proceedings of a Conference held in Heidelberg, September 10 - 14,
1984
These Proceedings have been assembled from papers presented at the
Conference on Models of Biological Growth and Spread, held at the
German Cancer Research Centre Heidelberg and at the Institute of
Applied Mathematics of the University of Heidelberg, July 16-21,
1979. The main theme of the conference was the mathematical
representation of biolog ical populations with an underlying
spatial structure. An important feature of such populations is that
they and/or their individual com ponents may interact with each
other. Such interactions may be due to external disturbances,
internal regulatory factors or a combination of both. Many
biological phenomena and processes including embryogenesis, cell
growth, chemotaxis, cell adhesion, carcinogenesis, and the spread
of an epidemic or of an advantageous gene can be studied in this
con text. Thus, problems of particular importance in medicine
(human and veterinary), agriculture, ecology, etc. may be taken
into consideration and a deeper insight gained by utilizing (more)
realistic mathematical models. Since the intrinsic biological
mechanisms may differ considerably from each other, a great variety
of mathematical approaches, theories and techniques is required.
The aims of the conference were (i) To provide an overview of the
most important biological aspects. (ii) To survey and analyse
possible stochastic and deterministic approaches. (iii) To
encourage new research by bringing together mathematicians
interested in problems of a biological nature and scientists
actively engaged in developing mathematical models in biology."
On March 8/9, 1976 a workshop on "Mathematical Models in Medicine"
was held at Mainz (German Federal Republic) by the group of "Mathe-
matical Models" of the Deutsche Gesellschaft fUr Medizinische Doku-
mentation, Informatik und Statistik. Purpose of this conference was
to bring together experts from the GFR and neighbouring countries
working in this field to evaluate possibilities and limits of this
area of research in discussions with interested participants. This
issue of Lecture Notes contains the invited contributions as well
as the relevan~ remarks made by the discussants. Corresponding to
the aims of the workshop the contributors had been encouraged to
demon- strate their mathematical models in the light of actual
applied examples. It had been our intention to restrict attention
to a small number of specific areas in order to achieve a
concentrated in depth treatment in these restricted areas. The
areas chosen contain two - Epidemio- logy and Cell Models - which
in the organisers feeling are not yet as well established in
Continental Europe and one - Pharmacokinetic- with a more direct
appeal to applied workers. While in the Epidemio- logy of
infectious and parasitic diseases today strategies of control and
eradication are gaining importance, the cell models are concerned
with explaining the modes of genesis of cancerous growth and the
kinetics and interactions within multi-cell structures.
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