Lectu re Notes in Biomathematics Managing Editor: S. Levin 57 Mathematics in Biology and Medicine Proceedings of an International Conference held in Bari, Italy, July 18-22,1983 Edited by V. Capasso, E. Grosso and S. L. Paveri-Fontana Springer-Verlag Editorial Board J. D. Cowan W Hirsch S. Karlin J. B. Keller M. Kimura S. Levin (Managing Editor) R. C. Lewontin R. May J. D. Murray G. F. Oster A. S. Perelson T. Poggio L. A. Segel Editors V. Capasso Dipartimento di Matematica, Universita di Bari Palazzo Ateneo, 70121 Bari, Italy E. Grossot Istituto di Igiene, Universita di Bari Policlinico, 70100 Bari, Italy S. L. Paveri-Fontana Istituto Universitario Navale Via Acton 38, 80133 Napoli, Italy AMS-MOS Subject Classification (1980): 34-XX, 35-XX, 45-XX, 60GXX, 60HXX, 60JXX, 60K99, 92-06 ISBN-l3: 978-3-540-J52(D-2 e-ISBN-13: 978-3-642-93287-8 001: 10.10071978-3-642-93287-8 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © by Springer-Verlag Berlin Heidelberg 1985 PREFACE These Proceedings contain a large part of the papers presented at the International Conference "Mathematics in Biology and Medicine" organized by the Dipartimento di Matematica and the Istituto di Igiene at the University of Bari, Italy, July 18-22, 1983. The main objective of the Conference was to bring together scientists in pure and applied mathematics and scientists in biology and medicine. The purpose was to exchange ideas and discuss the common problems encoun~red in the formulation, ana lysis and numerical treatment of mathematical models in the biomedical sciences. Si mulation methods and problems of validation of models vs. experimental data were al so treated. SUrveys on recent mathematical results motivated by biological questioffi were given. Altogether,we think that a balance between mathematical and biomedical aspects was maintained. The Scientific Committee consisted of E. Biondi (Milano), P. Colli-Franzone (Udine), I. Galligani (Bologna), M. Iannelli (Trento), G. Koch (Roma), E. Marubini (Milano), C. Matessi (Pavia), M. Primicerio (Firenze), L.M. Ricciardi (Napoli), R. Rinaldi (Milano), A. Zampieri (Roma), and the European Liaison Committee consisted of R.M. Anderson (United Kingdom), N.T.J. Bailey (Switzerland), O. Diekmann (The Netherlands), K. Dietz (F. R. Germany), K.P. Hadeler (F·. •. R. Germany), J.P. Kernevez (France). The Conference was made possible by support from the following institutions: Istituto Universitario Navale di Napoli, Universita di Bari, Consiglio Nazionale del le Ricerche - Comitato Nazionale per le Scienze Biologiche e Mediche, Comitato Na zionale per le Scienze Matematiche, Progetto Finalizzato Medicina Prevent iva e Ria bilitativa, IRMA Bari -, Regione Puglia, Provincia di Bari, Provincia di Taranto, Comune di Bari, Cassa di Risparmio di Puglia, Istituto S. Paolo di Torino, IBM-Ita lia. During five days, 19 general lectures were given and 77 contributed papers were presented, 10 of which being part of a poster session; 23 countries were represented through 148 scientists. We would like to thank all participants for their enthusiastic cooperation. It is a pleasure to acknowledge the help of the Local Organizing Committee. In oarticu lar we wish to thank G. Serio for the key work she has done during all stages of preparation and conduction of the Conference. The help of G. Galeone and L. Maddalena is also gratefully acknowledged. Finally we would like to mention tha~ as a conse quence of the severe space limitation on these Proceedings,the members of the Bari group in Mathematical Biology have kindly decided to submit elsewhere their contri butions to the Conference. Itisa great grief for us to mention that on May 10, 1984, during the final sta ges of preparation of this volume Professor Enea Grosso,our Co-Chairman, left us at the age of 62 years. We wish to remember him for his constant inspiration of new scientific work on the biomedical applications of mathematics. To Professor Grosso this volume is dedicated. We hope that young research63 will maintain his enthusiasm alive in developing and studying mathematical models for biomedical phenomena. It is our hope that with the help of modern methods of mathematical analysis and with the support of the revolutionary computer technology -- it will be possible to solve a growing number of challengingproblems in the biomedical sciences, brin ging mmkind to a better quality of life. v. Capasso S.L. Paveri-Fontana OBITUARY PROFESSOR ENEA GROSSO On May 10, 1984, the Fcientific community suffered a great loss with the sudden death of Professor Enea Grosso at the age of 62. It was a particular blow to the Ma thematical Epidemiology Group in Bari, which he had constantly encouraged to analyze open problems related to infectious diseases. Professor Grosso graduated from the University of Milan, his native city, in Medicine in 1949. He remained there as part of the School of Hygiene. His impor tant contributions to the field of atmospheric pollution, food and milk contamina tion, and the prevention of tuberculosis and polio gave him a very strong reputation in the Italian scientific community and also abroad, as he also spent much time in foreign universities during that period (he spent one year with Prof. A. Sabin at Cincinnati, and another period at the Institut "L. Pasteur" in Paris). With the recognition of the importance of his research in 1962 he was appoin ted Professor of Hygiene at the University of Camerino and in 1964 was called to the University of Bari, in Italy, and remained there for the rest of his life. After his arrival there, he devoted himself to the study of the endemic diseases of Bari and, more genera lly, of Puglia (the region containing Bari )and of the neighboring region of Basilicata. He soon became the central figure working on problems affecting the health of these two regions. Professor Grosso had always stressed the importance of primary prevention in the control of epidemics, and this stimulated him to look for new methods of analy zing epidemic systems. The search for answers to the tragic 1973 cholera epidemic, which spread throughout the Medi terranean area, led him to joint wt'rk with mathemat ic ians at the University of Bari (and in partlcclar the two editors of this volume) on the mathematical modelling of fecal-eral diseases. From 1978 until his death he was pert of the re search UTI i t of H..l hemat ica 1 Epidenoi 0 logy in the Spec ia 1 Programs "Prevent i ve Medicine" and "Control of Infectious DiseaseS' of the Italian National Research Council (Consiglio Nazionale delle Ricerche). (v.c.) LIST OF CONTRIBUTORS Ahmad R.: Department of Mathematics, University of Strathclyde, Gl lXH Glasgow Scotland. U.K. Alberghina L.: Cattedra di Biochimica Comparata, Facolta di Scienze, Universita di Milano, Via Celoria 26, 20133 Milano, Italy. Alt W,: SFB 123 Universitat, ,1m Neuenheimer Feld 293, D-6900 Heidelberg, F.R.G. Anderson R.M.: Department of Pure and Applied Biology, Imperial College, London Uni versity, London SW7 2BB. U.K. Aronson D.G.: University of Minnesota, School of Mathematics, 127 Vincent Hall, 206 Church Street S.E., Minneapolis, Minnesota 55455, USA. Audoly S,:lstituto di Matematica per Ingegneri, Universita, Viale Merello, 09100 Cagliari, Italy. Aulbach B.: Mathematisches Institut der Universitat, D-8700 WUrzburg, F.R.G. Banks H.T.: Division of Applied Mathematics, Brown University,Providenc~m~9Q, USA Barbi M.: Istituto di Biofisica, C.N.R., Via S. Lorenzo 26, 56100 Pisa, Italy. Barni N.: Istituto lnternazionale di Genetica e Biofisica, CNR, 80100 Napoli, Italy. Benham C.J.: Department of Mathematics, University of Kentucky, Lexington, KY, Usa 40506. Beretta E.: Istituto di Biomatematica, Facolta di Scienze, Universita di Urbino, Via A. Saffi 1, 61029 Urbino, Italy. Bernardi M.L.: Dipartimento di Matematica, Universita di Pavia, Strada Nuova 65, 27100 Pavia, Italy. Bertuzzi A.: Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185 Roma, Italy. Bohl E.: Universitat Konstanz, Fakultat fur Mathematik, D-7750 Konstanz 1, ~.F.G. Bozikov J.: Andrjia Stampar School of Public Health, Medical School, University of Zagreb, Zagreb, Yugoslavia. Bracht A.: Institut fUr Physiologische Chemie, Physikalische Biochemie und Zellbio logie der Universitat MUnchen, Goethestrasse 33, D-8000 MUnchen 2 F.R.G. Braumann C.A.: Universidade de Evora, 7000 Evora, Portugal. Bruni C.: Istituto di Automatica, Universita di Roma "La Sapienza", 00100 Roma,Italy. VIII Calvi Parisetti C.: Istituto matematico, Universita d~ Parma, Via Universita 12 43100 Parma~ Italy. Capelo A.C.: Laboratorio di Analisi Numerica del CNR, Corso Carlo Alberto 5 27100 Pavia, Italy. Caratozzolo F.: Biophysical and Electronic Engineering Division, Electrical Enginee ring Department, University of Genoa, Viale Causa 13, 16145 Genova, Italy. Cascino A.: Istituto Internazionale di Genetica e Biofisica,CNR, 80100 Napoli, Italy. Celentano F.C.: Dipartimento di Biologia, Sezione di Zoologia e Citologia, Via Ce loria 26, 20133 Milano, Italy. Chelazzi G.: Istituto di Zoologia dell'Universta di Firenze, Via Romana 17 50100 Firenze, Italy. Chiabrera A.: Biophysical and Electronic Engineering Division, Electrical Engineering Department, University of Genoa, Viale Causa 13, 16145 Genova, Italy. Chiang C.L.: University of California, Berkeley, California 94720 USA. Cipollaro M.: III Servizio Analisi, Seconda Scoola Medica, Universita di Napoli, 80100 Napoli, Italy. Clark C.W.: Department of Mathematics, University of British Columbia, Vancouver V6T 1W5 Canada. Clerico L.: Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30 00185 Roma,Italy. Cobelli C.: Istituto di Elettronica e di Elettrotecnica, Facolta di Ingegneria, Via Gradenigo 6/a, 35131 Padova, Italy. Colli Franzone P.: Istituto di Matematica, Informatica e Sistemistica dell'Universi ta di Udine, Via Mantica 1, 33100 Udine, Italy. Cooke K.: Pomona College, Claremont, California 91711, USA. Costa A.: Oncologia Sperimentale C, Istituto Nazionale per 10 Studio e la Cura dei Tumori, 20100 Milano, Italy. Cvjetanovic B.: Andrjia Stampar School of Public Health, Medical School, University of Zagreb, Rockfellerova 4, 41000 Zagreb. Dal Passo R.: Istituto per le Applicazioni del Calcolo "M. Picone", CNR, Viale Poli clinico 137, 1-00161 Roma, Italy. I D'Angio L.: Istituto Matematico, Universita di Cagliari, Via Ospedale 72, 09100 Ca- gliari, Italy. Del Bino C.: Oncologia Sperimentale C, Istituto Nazionale per 10 Studio e la Cura dei Tumori, 20100 Milano, Italy. Del Grosso G.: Dipartimento ~i Maternatica, Universita degli Studi di Roma "La Sapien za", Piazzale A. Moro 5, 00185 Roma, Italy. Delimar N.: Immunoloski Zavod, Zagreb 41000, Yugoslavia. De Mottoni P.: Istituto di Matematica Applicata, Universita, 67.1.00,L'Aquila, Italy. IX Deneubourg J.L.: Service de Chimie-Physique II ULB, Campus Plaine, Bruxelles, Belgium. Dezelic G.: Andrjia Stampar School of Public Health, Medical School, University of Zagreb, Rockfellerova 4, 41000 Zagreb. Dick G.: Zoologisches Institut der Universitat zu Koln, Weyertal 119, 5000 Koln 41, Bundesrepublik Deutschland. Di Cola G.: Istituto di Matematica, Universita degli Studi di Parma, Via universi ta 12, 43100 Parma, Italy. Diekmann 0.: Mathematisch Centrum, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands. Dietz K.: Institute of Medical Biometry, Tlibingen University, Westbahnhofstrasse 55, 7400 Tlibingen 1, F.R.G. Doedel E.: Computer Science Department, Concordia University, 1455 de Maisonneuve, Blvd. W. Montreal, Quebec H3G IM8, Canada. Dvorak I.: Center of Biomathematics, Institute of Physiology, Czech. Acad. Sci., Prague 4, Eisenfeld J.: Department of Mathematics, University of Texas at Arlington, Arlington, 76019 Texas. Ferrante L.: Istituto di Medicina Sperimentale e Clinica, Universita di Ancona, 60100 Ancona, Italy. Focardi S.: Istituto Nazionale di Biologia della Selvaggina, Via Stradelli Guel fi 23/a, Ozzano Emilia (Bologna), Ital~ Franze A.: Istituto Internazionale di Genetica e Biofisica, CNR, 35100 Padova, Italy. Gandolfi A.: Istituto di Analisi dei Sistemi ed Informatica del CNR, Via Manzoni 30, 00185 Roma, Italy. Gastaldi L.: Dipartimento di Matematica, Universita degli Studi di Pavia, Strada Nuo va 65, 27100 Pavia, Italy. Germani A.: Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 3C 00185 Roma, Italy. Grattarola M.: Dipartimento di Ingegneria Biofisica ed Elettronica, Via dell'Opera Pia lla, Universita di Genova, 16145 Genova, Italy. Gripenberg G.: Institute of Mathematics, Helsinki University of Technology, SF-02150 Espoo 15, Finland. Grossman Z.: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. Gyllenberg M.: Helsinki University of Technology, Institute of Mechanics, SF-0215C Espoo 15, Finland. Hadeler K.P.: Lehrstuhl fur Biomathematik der Universitat Tlibingen, Institut fur Biologie II, Auf der Morgenstelle 28, 7400 Tlibingen 1, Deutschland. Henry J.: INRIA, Domaine de Voluceau BP 105 - Rocquencourt, 78153 Le Chesnay Cedex, France. x Holden A.V.: Department of Physiology, University of Leeds, Leeds LS2 9JT, U.K. Iapnelli M.: Istituto Matematico, Facolta di Scienze, Universita degli Studi di Trento, 38050 Povo di Trento (Trento), Italy. Ishii H.: Department of Mathematics, Chuo University, Tokyo 112, Japan. Kareiva P.: Division of Biology and Medicine, Brown University, Providence, RI 02912, USA. Kernevez J.P.: Universite de Technologie de Compiegne, Department de Mathematiques. Appliquees et d'informatique, BP 233, 60206 Compiegne Cedex, France. Kindlmann P.: Centre of Biomathematics, Institute of Entomology, Na Sadkach 702, 370 05 Ceske Budejovice, Czechoslovakia. Koch G.: Dipartimento di Matematica, Istituto Matematico "G. Castelnuovo", Piazzale A. Moro 5, 00185 Roma, Italy. Kosicek M.: Immunoloski Zavod, Zagreb 41000, Yugoslavia. Kubinova L.: Center of Biomathematics, Institute of Physiology, Czech. Acad. Sci., Prague 4, Videnska 1083, Czechoslovakia. Lakshmikantham V.: Department of Mathematics, University of Texas at Arlington, Arlington, 76019 Texas, USA. Lambrecht R.M.: Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973, USA. Lamm P.K.: Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA. Lazzari C.: Istituto di Biomatematica, Facolta di Scienze, Universita di Urbino, Via A. Saffi 1, 61029 Urbino, Italy. Lefevre C.: Universite Libre de Bruxelles, Campus Plaine, C.P. 219, B-1050 Bruxelles, Belgique. Lolli E.: Dipartimento di Matematica, 2° Universita degli Studi, Via Orazio Raimondo, 00173 Roma, Ital~. Longini I.M.: Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, 48109,USA. Macchiato M.: Istituto Internazionale di Genetica e Biofisica, CNR, 80100 Napoli. Italy Malice M.P.: Universite Libre de Bruxelles, Campus Plaine, C.P. 219, B-1050 Bruxelles, Belgique. Marchetti F.: Dipartimento di Matematica, Universita di Roma "La S.apienza" Piazzale A. Moro 5, 00185 Roma, Italy. Mariani L.: Istituto di Elettrotecnica ed Elettronica dell'Universita and LADSEB-CNR, 35131 Padova, Italy. Matis J.H.: Institute of Statistics, Texas A&M University, College Station, Texas 77843, USA. Mazzini G.: Istituto di Automatica, Universita di Roma "La Sapienza",00185 Roma, Italy.