Mathematical Biology Seminar, Fall 1997
Department of Mathematics,
Arizona State University
CO-SPONSORED BY THE CENTER FOR
SYSTEMS SCIENCE AND ENGINEERING
Confirmed Talks
Friday, September 5, 2:40pm-3:30pm,
PSA 307: Hal Smith, Department of Mathematics, ASU
Effects of random motility on microbial growth and competition in a plug
flow reactor
Friday, September 12, 2:40pm-3:30pm,
PSA 307: Kewei Chen, Good Samaritan Regional Medical Center(PET
center) and Department of Mathematics ASU
PET: Images of real life and its mathematical challenges
ABSTRACT: First, a brief introduction will be given to the exciting new
discoveries using PET on many different parts of our human body including
the brain. Then, the critical role of mathematics will be reviewed in the
PET success story. Finally, focus will be on the list of some potential
challenges in PET that call for help from mathematicians.
Friday, September 19, 2:40pm-3:30pm,
PSA 307: Angela Stevens, University of Heidelberg, presently Stanford
University. Joint Mathematical Biology and Control Theory Seminar (co-sponsored
by the Center of Systems Science)
Self attracting random walks and their relation to aggregation phenomena
in biology
ABSTRACT: Gathering of individuals is a widespread phenomenon in biology.
Reasons are, for instance, to give each other shelter, to reproduce, to
explore new regions, to feed or to endure starvation conditions. In many
cases the process of aggregation occurs via exchange of attractive signals
between the individuals. To understand the interplay between single particle
behavior and many particle aggregation, random walk models for the localization
of a single particle due to an attracting reinforced signal are introduced.
The production rate of the signal plays a crucial role for localization.
The continous approximations of these random walks nicely reflect these
conditions. Aggregation of many particles instead requires stronger attraction
of the individuals by the signal than localization of a single particle,
if their interaction is only local. It could be shown that this is not
the case if the particles interact moderately. During the talk the qualitative
behavior of the random walk models and their continous approximations with
respect to aggregation are discussed.
Friday, September 19, 3:40pm-3:30pm,
PSA 307: Stephan Luckhaus, University of Bonn, presently Stanford
University. Joint Mathematical Biology and Control Theory Seminar (co-sponsored
by the Center of Systems Science)
Detecting Edges in Images
ABSTRACT: The talk focusses on a continuum model for gray value pictures.
The basic assumption is that the gray values are given by a BV function
on a domain in the plane. This function cannot be assumed to be continuous.
Extraction of the jump set is important as well for processing of the images
as for reconstruction from noisy data. There exist two approaches to this.
The first is variational based on the Mumford-Shah functional, the second
is a nonlinear filtering method. An algorithm for the extraction of the
jump set equivalent to the Mumford-Shah approach will be presented with
only O(n) operations.
Friday, September 26, 2:40pm-3:30pm,
PSA 307: Kewei Chen, Good Samaritan Regional Medical Center(PET
center) and Department of Mathematics ASU
Tracer Kinetic Modeling Technique in PET
ABSTRACT: PET kinetic modelling technique starts with the construction
of an appropriate mathematical model for a biological process of interest.
In the first part of the talk, the model building is covered using a C-11
acetate dynamic as an example. Then, we will discuss how the kinetic modeling
technique is used to estimate parameters. Various potential applications
will be mentioned.
Friday, October 3, 2:40pm-3:30pm,
PSA 307: Yang Kuang, Mathematics Department, ASU.
Modeling and Analysis of a Marine Bacteriophage Infection
Friday, October 10, 2:40pm-3:30pm,
PSA 307: Xiao-Qiang Zhao, Mathematics Department, ASU.
Multi-Species Competition in a Periodic Chemostat
ABSTRACT: The chemostat is an important laboratory apparatus " used for
the continuous culture of microorganisms. In ecology it" is often viewed
as a model of a simple lake system, of the " wastewater treatment process,
or of biological waste " decomposition. Various mathematical models have
been developed" and analyzed extensively by many different investigators(see,
" e.g., H. Smith and P. Waltman, Cambridge University Press, 1995). In
this talk, we will present a general framework to study," analytically,
models of n-species competition in a periodically" operated chemostat.
Nutrient input, dilution and species specific" removal rates are all permitted
to be periodic (but of commensurate" period). As well, each species specific
nutrient uptake function" is assumed to be a monotone increasing function
of the substrate" concentration, but can be periodic as a function of time
(but" again of commensurate period). Differential species specific" removal
rates are also permitted. We apply the comparison method," abstract persistence
theory for periodic semiflows (see X.-Q. Zhao," Canad. Appl. Math. Quart.,
3(1995), 473-495) and the asymptotically" periodic semiflow theory(see
X.-Q. Zhao, Commun. Appl. Nonl. Anal.," 3(1996),43-66) to determine criteria
that guarantee the existence" of at least one positive periodic solution
for the full system and" the uniform persistence of all of the interacting
species. For " 3-species competition, in the case that all the species
specific" removal rates are assumed to be equal to the dilution rate, under"
additional assumptions on the form of the attractors in the lower" dimensional
subsystems, we further get natural invasibility " conditions. Some of the
improved results also give sufficient" conditions for competition mediated
coexistence of three species.
Friday, October 17, 2:40pm-3:30pm,
PSA 307: Jiaxu Li, Mathematics Department, ASU.
Modeling and Analysis of Glucose-Insulin Interaction
ABSTRACT: In the last three decades, several models on the interaction
of glucose and insulin have appeared in the literature, the mostly used
one is generally known as the "minimal model" which was fisrt published
in 1979. Recently, this minimal model is being questioned by De Gaetano
and Arino(1997) from both physilogical and modeling aspects. Instead, they
proposed a new and mathematically more reasonable model, called "dynamic
model". The objective of this work is to put this dynamic model in a more
general and robust setting and perform a detailed qualitative analysis
of such models. We shall also perform necessary simulations and point out
some important implications.
Friday, October 24, 2:40pm-3:30pm,
PSA 307: Zhilan Feng Mathematics Department, Purdue University.
Mathematical Models for the Disease Dynamics of TB
ABSTRACT: A series of models are developed to determine possible mechanisms
that may allow for the survival and spread of naturally resistant strains
of TB as well as antibiotic- generated resistant strains of TB, and to
study the impact of exogenous reinfection on the recently observed resurgence
of TB. We show that non-antibiotic co-existence is possible but rare for
naturally resistant strains while co-existence is almost the rule for strains
that result from the lack of compliance with antibiotic treatment by TB
infected individuals. It is also shown that exogenous reinfection has a
drastic effect on the qualitative dynamics of TB.
Friday, October 31, 2:40pm-3:30pm,
PSA 307: Marcos Lizana Mathematics Department, University of Los
Andes.
A Spatially Discrete Model for Aggregating Population
Friday, Nov. 7, 2:40pm-3:30pm,
PSA 307: Horst Thieme Mathematics Department, ASU.
Optimal Emigration Strategies in a Size-Structured Metapopulation
Model
Friday, Nov. 14, 2:40pm-3:30pm,
PSA 307: Frank Hoppensteadt Mathematics Department, ASU.
TBA
ATTENTION: TIME and Place changes:
Thursday, Nov. 20, 2:40pm-3:30pm, GWC 604: Fred Bruaer Mathematics
Department, University of Wisconsin.
A Model for Communicable Diseases with Age-Dependent Mortality
ABSTRACT: We formulate a model for the transmission of communical diseases
in a population with a density-dependent birth rate and an age-dependent
death rate. We examine the basic reproductive number, stability of disease--free
and endemic equilibria, and the relation between the basic reproductive
number and mean age at infection. The model is constructed directly as
a system of Volterra equations, without examination of a fully age-structured
model.
ATTENTION: TIME and Place changes:
Monday. Dec. 1, 2:40pm-3:30pm, GWC 604: Kathleen Crowe Mathematics
Department, Humboldt State University.
Depth-Profile Models in Marine Plankton Systems