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