Evolution of a mathematical model of an aggressive–invasive cancer under chemotherapy

In this work, we first propose continuous models of an aggressive–invasive cancer which is characterized by its heterogeneity, by its high proliferation rates and by the potential invasion of cancer cells into surrounding tissue. An acidification environment mechanism is included in the models to analyze the level of invasion. Second, we introduce and analyze their discrete versions obtained by an appropriate discretization. Afterwards a chemotherapy treatment with a gradual effect is added, which includes important aspects as resistance and drug toxicity. Finally we make comparisons among different chemotherapy schemes to identify a suitable combination in order to eradicate or to reduce the growth of the tumor.