Mathematical Biology Seminar

Seminar information archive ~03/28Next seminarFuture seminars 03/29~


2016/04/26

15:00-16:00   Room #128演習室 (Graduate School of Math. Sci. Bldg.)
Lev Idels (Vanvouver Island University)
Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)
[ Abstract ]
In general, delay differential equations provide a richer mathematical
framework (compared with ordinary differential equations) for the
analysis of biosystems dynamics. The inclusion of explicit time lags in
tumor growth models allows direct reference to experimentally measurable
and/or controllable cell growth characteristics. For three different
types of angiogenesis models with variable delays, we consider either
continuous or impulse therapy that eradicates tumor cells and suppresses
angiogenesis. It was shown that with the growth of delays, even
constant, the equilibrium can lose its stability, and sustainable
oscillation, as well as chaotic behavior, can be observed. The analysis
outlines the difficulties which occur in the case of unbounded growth
rates, such as classical Gompertz model, for small volumes of cancer
cells compared to available blood vessels. The Wheldon model (1975) of a
Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of
recent discovery that this model has a major drawback.
[ Reference URL ]
https://web.viu.ca/idelsl/