The recent tumor research has lead scientists to recognize the central role played by cancer stem cells in sustaining malignancy and chemo-resistance. A model of cancer presented by one of us describes the mechanisms that give rise to the different kinds of cancer stem-like cells and the role of these cells in cancer diseases. The model implies a shift in the conceptualization of the disease from reductionism to complexity theory. By exploiting the link between the agent-based simulation technique and the theory of complexity, the medical view is here translated into a corresponding computational model. Two main categories of agents characterize the model, 1) cancer stem-like cells and 2) stem cell differentiation stage factors. Cancer cells agents are then distinguished based on the differentiation stage associated with the malignancy. Differentiation factors interact with cancer cells and then, with varying degrees of fitness, induce differentiation or cause apoptosis. The model inputs are then fitted to experimental data and numerical simulations carried out. By performing virtual experiments on the model's choice variables a decision-maker (physician) can obtains insights on the progression of the disease and on the effects of a choice of administration frequency and or dose. The model also paves the way to future research, whose perspectives are discussed.