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.