Fix the parameter r = 1 and vary the parameter k from 0.5 to 3.0. Next fix k = 1.5 and vary r from 0.5 to 4.0. Describe the results of your experiments from the biological viewpoint.
Load the image into your PHASER by clicking on the picture.
This picture is not to scale. Adjust the Window size to get a true aspect ratio
and draw the Direction Field.
Using the Direction Field and solution curves answer the following questions.
Explain what this model predicts for the tumor growth.
Experiment with several different initial tumor sizes.
How does the future size of tumor depend on its initial size?
Experiment with several values of the parameters a and b.
Explain the roles of these parameters in the tumor growth.
Consult the famous article "Dynamics of Tumor Growth" by A.K. Laird in
British Journal of Cancer (1964) 18, 490-502. doi:10.1038/bjc.1964.55
Verify that the formula for Gompertz curve x = x_0 exp((a/b)(1 - exp(-bt))
that she gives in this article satisfies Gompertz's differential
equation above.