Mathematical modeling of cancer-immune interactions: agent-based and continuous modeling reveal novel, non-monotonic patterns

The study of cancer-immune dynamics is broad. There are myriad instances of these dynamics and much heterogeneity among the two. To explore these relationships in their fullness, mathematical modeling is used to go further faster than can be done by experiments alone. In this work, two models of cancer-immune dynamics are explored and their applications to clinical settings are predicted. The mathematical techniques are also exposited. The first model looks at epithelial-to-mesenchymal transition in epithelial cancers and the effects on progression and invasive disease. We find and validate evidence that key parameters in this process control the time to invasion in non-monotonic ways. The second model studies the newly discovered relevance of B cells to immune checkpoint therapy in two skin cancers: melanoma and BCC. We find an explanation for the difference in response rates between the two cancers as well as a means to assess the sustained effects of immunotherapy be a single sample of cells. Finally, we utilize a nascent tool for parameter inference and show how it could be applied to an ODE model and show the types of results such a tool can produce