FRIDAY, February
6,
Horst Thieme, Department of Mathematics "Persistence
and Permanence in Non-autonomous Systems" FRIDAY, February
6,
Horst Thieme, Department of Mathematics "Persistence
and Permanence in Non-autonomous Systems"FRIDAY, February 13,
Steve Baer, Department of Mathematics
FRIDAY, February 20,
MATHEMATICAL BIOLOGY SEMINAR PSA 302 10:40 a.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Linda Allen, Texas Tech
University
"Deterministic and Stochastic Discrete-time Epidemic Models"
ABSTRACT: The dynamics of
some deterministic and stochastic
discrete-time epidemic models
are analyzed and compared. In the
deterministic models, the
disease is eliminated from the
population if the basic
reproduction number $R_0<1$ and the
disease persists if $R_0>1$.
However, in the stochastic models,
it is shown that there is
a positive probability the disease is
eliminated, regardless of
the magnitude of the basic
reproductive number. In
fact, the probability that the number
of infectives is zero satisfies
$p_0(t)>0$ for any time $t$
and $\lim_{t\rightarrow
\infty} p_0(t)=1$. If the probabilities
in the stochastic models
are conditioned on nonextinction, then,
if $R_0>1$, there exists
a quasi-stationary probability
distribution that exhibits
behavior similar to the deterministic
models.
FRIDAY, February 27,
MATHEMATICAL BIOLOGY SEMINAR PSA 302 10:40 a.m.
Xiaoqiang Zhao, Department of Mathematics
"Uniform Persistence and Coexistence States in Dissipative
Biological Systems"
ABSTRACT: In this talk,
we will discuss the existence of
coexistence states, abstract
and practical persistence and
their perturbations in dissipative
biological systems. Some
illustrative examples from
population dynamics will also be given
FRIDAY, MARCH 27, 1998
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MATHEMATICAL BIOLOGY SEMINAR
PSA 302 10:40 a.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Hal Smith, Department of
Mathematics
"A Model of Microbial Competition for Nutrient and for Wall
Sites in a Plug Flow Reactor"
FRIDAY, April 10, 1998
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MATHEMATICAL BIOLOGY SEMINAR
PSA 302 10:40 a.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Edoardo Beretta, University
of Urbino, Italy
"A SRI Model with Time Delays: Local and Global Stability
Results"
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FRIDAY, April 17, 1998
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MATHEMATICAL BIOLOGY SEMINAR
PSA 302 10:40 a.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Tanya Kostova, Institute
of Mathematics & Computer Science,
Bulgarian Academy of Sciences
"Comparing Two Simple Models for Competition between Age Classes"
FRIDAY, April 27, 1998
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MATHEMATICAL BIOLOGY SEMINAR
A model for wolf territories and wolf-deer interactions.
Mark A. Lewis,
Department of Mathematics
University of Utah
Field studies in Northeastern Minnesota indicate that wolf (Canis
lupus) territory patterns are clearly defined and that the spatial
distribution of white-tailed deer (Odocoileus virginianus) is strongly
affected by the wolf territories. In this work, wolf movement
is modeled with a system of partial differential equations coupled
to ordinary differential equations describing scent-marking behavior.
No assumptions are made about the territories themselves. Analysis
of
the model, however, indicates that territorial patterns arise
naturally as stable stationary solutions. `Walls' of scent marks
define the edges the territory, and `buffer zones' are found
between territories. Model results are compared with radio-tagging
data.
Lastly, the effect of resulting wolf distributions on the deer
population is considered. Results from the mathematical model
reflect field observations: deer are found primarily in buffer
zones between the wolf-pack territories.