Investigation of a mathematical model describing global cancer growth and treatment: An inhomogeneous model based on the generalized logistic equation

Abstract

Tumor growth is manifestation of the evolution of a complex system. Researchers have limited scope of modelling studies on specific aspects or stages of the process. It has led to unsatisfactory explanation of clinical observations. We hereby demonstrated that an inhomogeneous model built on the generalized logistic equation could serve better. It was developed to describe the whole process of tumor progression, clinically observed independence of index tumor growth from spread of the disease and growth deceleration during early stage of solid tumors. It was validated by simulating the coexistence of exponential and sigmoidal growth in chronic lymphocytic leukaemia, theories of tumor heterogeneity, as well as by accommodating notions pertaining to tumor treatment and prognosis. We thought therefore it was an interesting and not unjustifiable description of actual tumor growth in human body and hoped it might encourage more researchers to look at tumor modelling from a clinical perspective.