The Gompertz model is a classical model of tumour growth where a is a growth rate and b is the carrying capacity (maximal population) of the tumour. The model is given by d dt x(t) = ax(t) log(bx(t)). Find and characterise the equilibria as a function of the model parameters a and b.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The Gompertz model is a classical model of tumour growth where a is a growth
rate and b is the carrying capacity (maximal population) of the tumour. The model
is given by
d
x(t) = ax(t) log(bx(t)).
Find and characterise the equilibria as a function of the model parameters a and b.
Transcribed Image Text:The Gompertz model is a classical model of tumour growth where a is a growth rate and b is the carrying capacity (maximal population) of the tumour. The model is given by d x(t) = ax(t) log(bx(t)). Find and characterise the equilibria as a function of the model parameters a and b.
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