Texts:
The deterministic Gompertz model ππ/ππ‘ = [ππ(log[πΎ/π]) β πΈπ], π(π‘0) = π0 > 0, is widely used to describe the volume of large tumor cells. In this model, the constant π is related to the proliferative ability of the tumor cells, πΈ is a constant related to treatment/therapy rate, and πΎ is the carrying capacity.
To solve the deterministic model, we can use the transformation π(π) = log(πΎ/π).
b. Now, let's assume that the volume dynamic can be modeled under a continuous spectrum of disturbances in the growth rate π, such that π fluctuates about a mean value π as π β‘ π + ππ(π‘).
Department of Mathematics
Augusta University
Show that the resulting stochastic differential equation from the disturbances is ππ = [ππ(log[πΎ/π]) β πΈπ]ππ‘ + ππ(log[πΎ/π])ππ(π‘), π(π‘0) = π0 > 0, where π(π‘)ππ‘ = ππ(π‘).