2011-Barbarossa, Maria.. 2011. Delay models for cancer and tumor growth. PowerPoint Slides.

By Brian Winkel

SIMIODE, Cornwall NY USA

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Abstract

Barbarossa, Maria.. 2011. Delay models for cancer and tumor growth. PowerPoint. 81 slides.

From the slides:

Background: Delay Equations

     Ordinary vs. Delay Differential Equations

     Applications in Biology

     Stability Analysis for DDEs

Delay Equations for Tumor Modelling

     Few Different Models

     Models based on the cell cycle

     Time delays in the immune response

Let us sum up the main ideas of today’s lecture:

Delay equations for a better description of the real-life phenomenon

Delay models better than ODE-models reproduce observed dynamics or measured data (e.g. oscillatory and chaotic behavior)

For the analysis of constant delay problems we can exploit the theory of ODEs

Numerical implementation is easier (and faster to compute) compared to PDE-problems

Delays in tumor modelling can arise from

     the “spatiality” of the problem

     regulation processes

     activation and reaction of the immune system

Keywords: cancer, tumor, growth, stability, differential equation, model

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Researchers should cite this work as follows:

  • Brian Winkel (2017), "2011-Barbarossa, Maria.. 2011. Delay models for cancer and tumor growth. PowerPoint Slides.," https://www.simiode.org/resources/4040.

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