The Hallmarks of Mathematical Oncology

Over the past 25 years, there has been an unparalleled increase in understanding of cancer biology. This transformation is exemplified by Hanahan and Weinberg’s decision in 2011 to expand their original Hallmarks of Cancer from six traits to ten! At the same time, mathematical modeling has emerged as a natural tool for unraveling the complex processes that contribute to the initiation and progression of cancer, for testing hypotheses about experimental and clinical observations and assisting with the development of new approaches for improving its treatment. This article starts by reviewing some of the earliest models of tumor growth and tumor responses to radiotherapy. Following Hanahan and Weinberg’s lead, attention then focuses on how closer collaboration with cancer scientists and access to experimental data are stimulating the development of new and increasingly detailed models that account, for example, for tumor–immune interactions and immunotherapy. The article concludes by discussing the ways in which mathematical modeling is being integrated with experimental and clinical studies, and outlining how this could improve disease diagnosis and the delivery of effective personalized treatments to cancer patients. As such, this article serves as an introduction to mathematical modeling of cancer and its treatments, suitable for researchers seeking to enter the field.