J. Math. Biol. (2006) 53:491–495
DOI 10.1007/s00285-006-0025-y
Mathematical Biology
Preface
Thomas Hillen · Frithjof Lutscher ·
Johannes Müller
Published online: 18 August 2006
© Springer-Verlag 2006
It is an honor and a pleasure to congratulate our teacher, mentor and friend
Karl-Peter Hadeler to his 70th birthday. It is exciting to see so many colleagues
and friends join us for this occasion with research articles in this special issue
of the Journal of Mathematical Biology. We are thankful to Springer to make
this issue possible.
When K.P. Hadeler took up university studies in mathematics and biology in
1956, the interdisciplinary field of mathematical biology was not yet “invented”
Fig. 1 K.P. Hadeler in the
1960s
T. Hillen (B)
Edmonton, Canada
e-mail: [email protected]
F. Lutscher
Ottawa, Canada
J. Müller
Munich, Germany
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T. Hillen et al.
Fig. 2 a Coffee at K.P. Hadeler’s home in Tübingen. From left to right: J. Müller, H. Hadeler,
K.P. Hadeler, T. Hillen, L. Alaoui, H. Mwambi, J. von Below, b K.P. Hadeler and his two last PhD
students to graduate from Tübingen: D. Schieborn and J. Braun
(although research in the area was certainly done). Would he have dreamt
in those days that he himself would be a pioneer in bringing his two subjects together and help shape the emergent discipline? When he had to decide
between the two subjects, he chose to write his dissertation in mathematics
with L. Collatz at the University of Hamburg, where he graduated in 1965.
Even before he finished his Ph.D., his first papers were published in Russian
(!), while he was studying in Moscow.
After his Habilitation in Hamburg (1967) and professorships in Minnesota,
Nijmegen, and Erlangen, he became full professor in Tübingen in 1971, first in
biology, and then in 1973 also in mathematics. After almost 30 publications in
mathematics, it was also in 1973 that he published his first paper in mathematical biology on “Models for selection in population genetics”. While research
articles on numerics, matrices and eigenvalue problems continue to appear,
much of his focus was now on the interdisciplinary field of biomathematics.
He co-founded the Journal of Mathematical Biology (1974) and instigated the
Oberwolfach conferences in mathematical biology (1975). A more detailed
account about how he shaped the field is given by Simon Levin in this volume.
At home in Tübingen, K.P. Hadeler developed and taught courses for
biologists as well as for mathematicians, and he wrote a book on mathematics
for biologists. With his enthusiasm for the subject, he got a large number of students interested in the subject and took on the role of a supervisor and mentor.
His students were pushed hard to understand things in more detail, to extend
and expand the analysis, and to view the larger picture, but then he stood back
and let us have the recognition for the work that would not have been possible
without him. He cared for us students, wrote countless reference letters, and
found money for us to go to conferences or to extend funding for the time necessary to finish our work. After graduation, he never let us go without knowing
that we will be going to a “good” place. Currently, at least 9 of his more than 20
PhD students hold academic positions in Europe and North America.
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Even after his official retirement from the University of Tübingen, he continues to inspire colleagues and students alike throughout the world. His incredible
memory and his ability to see (mathematical and biological) connections in the
“bigger picture” provide an invaluable resource to all who work with him.
It is hard, if not impossible, to list all the fields in which K.P. Hadeler made
contributions, even more so since his work spans several disciplines. Nonetheless, we think that even an incomplete list is better than none, and we apologize
if we missed an area.
The more mathematical aspects of his work can loosely be put into two
categories: (1) Operator Theory (linear and nonlinear eigenvalue problems,
normal and positive operators, numerical methods, and variational problems),
and (2) Dynamical Systems (reaction–diffusion equations, delay equations,
quasimonotone systems, Schrödinger equations, transport equations, and cellular automata).
On the biological side, his interests include, but are not limited to, genetics
and selection, parasite models, epidemic models (in particular structured population models, vector transmitted diseases, HIV and AIDS models, vaccination
strategies, spread of diseases), individual movement and spatial spread (for
example random walk models, traveling waves), chemostat, and proteasomal
cleavages.
Additionally, he recently published papers on granular matter.
The contributions to this volume reflect the wide variety of K.P. Hadeler’s
research interests. The researchers contributing stand for the large number of
friends and collaborators as well as for the mathematical community that widely
recognizes the significance of his work. We briefly introduce the individual articles.
• Colijn, Fowler, and Mackey take a twofold approach in understanding certain hematological diseases in which the cell count of several blood cells
oscillates at different frequencies, in particular where there appear high-frequency oscillations at the peak of lower-frequency cycles. First they show by
using transform methods on the data that these oscillations are real and not
just noise. Then they use a system of delay differential equations together
with parameter estimates from experiments and show that similar patterns
can be observed.
• In most of the literature on structured populations, the model parameters
are assumed to be constant in time. Cushing investigates the question how
the predictions of a model change when the parameters become periodic
functions, as is often the case in nature. Particularly important is the question
whether the average value required for population persistence is higher or
lower than without oscillations.
• The paper by Esteva, Rivas, and Yang investigates the effects of predation
of mosquitoes by water mites. They find the possibility of coexistence of the
two species under appropriate conditions and investigate the stability of the
corresponding equilibrium.
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• The paper by Hesseler, Schmidt, Reichl, and Flockerzi combines experiment
and mathematical modeling and analysis when in a chemostat a metabolic
by-product affects two competing species differently. The effect is that in
addition to the well-known exclusion principle, bistability and stable coexistence are found, depending on the parameter regime. Julia Hesseler was
K.P. Hadeler’s last Diploma student in Tübingen.
• Hillen develops mathematical models for cell movement in fibre networks.
Based on experimental observations of metastatic cancer cells that move
through collagen tissues, a transport equation formalism is used. Macroscopic advection–diffusion equations are derived by scaling methods, where
the mean drift velocity corresponds to the mean fibre orientation and the
diffusion tensor corresponds to the variance-covariance matrix of the fibre
orientational distribution.
• Iida, Mimura, and Ninomiya study the effect of competition mediated cross
diffusion on the stability of coexistence equilibria. They show that a certain class of cross-diffusion competition models can be approximated by a
(larger) system of reaction–diffusion equations. It turns out that cross-diffusion induced instabilities correspond to Turing instabilities of the approximative system.
• Martcheva, Thieme and Dhirasakdanon provide a novel mathematical
approach to Kolmogorov’s differential equations on parasitic infections
by constructing the solution semigroup on an appropriate sequence space.
These systems of equations arise not only from parasite models, but in
general from patch models for populations and also from Markov chains.
Conditions for extinction or persistence of a population are given.
• In the paper by Müller, Kuttler, Hense, and Rotballer the influence of spatial
structure on the behavior of microorganisms is elaborated. They investigate
the communication between single cells. The regulatory networks within
cells are coupled via linear parabolic equations reflecting the diffusion of
signaling molecules. Comparison methods yield results about the asymptotic
behavior of solutions, and approximation methods adapted from modulation equations allow for the investigation of communication distances using
experimental images generated by confocal laser scanning microscopy.
• The interpretation of backward bifurcations in epidemic models attracted
more and more attention in recent years. Safan, Heesterbeek, and Dietz
develop a generalization of the reproduction number concept that is capable
to give reliable information about endemic equilibria even if the reproduction number fails to do so. They consider the most simple situation (an SIS
model) in order to focus on concepts instead of technique. It is expected
that the result can be generalized to a wide class of models.
• Shim, Feng, Martcheva, and Castillo-Chavez contribute to the theory of
epidemics and the investigation of control strategies. They develop and
investigate an age structured model for rotavirus. A threshold theorem
is proven, optimal vaccination strategies are determined and a numerical
scheme for this epidemic model is developed. On the basis of this paper it
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Fig. 3 Helgard and Karl
Hadeler at their home in
Tübingen
may be eventually possible to establish practical guidelines for vaccination
campaigns against the rotavirus.
• Smith considers monotonic decomposable maps. These maps can be decomposed into an increasing and decreasing part. This can be used as an advantage to understand the asymptotic behavior of the system. Decomposable
maps appear as population models in various areas of mathematical biology.
H. Smith gives an example of a structured population.
Dear Karl, we hope you will continue to inspire students and colleagues
alike. We are looking forward to further fruitful collaborations and wish you all
the best for the future.
Alles Gute und vielen Dank
Thomas Hillen, Frithjof Lutscher, Johannes Müller