A stochastic Gompertz model highlighting internal and external therapy function for tumour growth

摘要

This paper proposes a model of tumour cell growth based on a Gompertz-type nonhomogeneous stochastic diffusion, whose drift coefficient depends on two functions of time that influence the dynamic behaviour of the model, and which can be interpreted in the context of this type of cell growth. The first of these time functions is an immunologic endogenous therapy factor, and the second is an exogenous therapy factor that models the dynamics of an externally controllable treatment on tumour growth. We establish the basic probabilistic characteristics of the model from the corresponding Itô differential equation, explicitly obtaining the expression of the trend functions. We then study the functional aspects and computational statistics associated with the maximum likelihood estimation of the model parameters. Finally, we provide a detailed discussion of the inter-relationships between the internal parameters of the diffusion process and the overall diffusion coefficient of the model.