IntroductionMathematical modeling has become a valuable tool in the continued effort to understand, predict and ultimately treat a wide range of cancers in recent years [1,2]. By describing biological phenomena in the concise and formal language of mathematics, it is possible to elucidate key components of complex systems and ultimately develop tools capable of quantifying and predicting system behavior under given conditions. When these tools are applied as a complement to the detailed understanding of cancer biology provided by biological scientists and clinicians, new insights can be gained into the mechanisms and first-order principles of cancer development and control [3].To date, although mathematical tools have been applied extensively in understanding tumor growth and dynamic interactions between cancer and host, studies involving the theoretical modeling of patient response to treatment and the contribution of such findings to the development of clinically-actionable therapeutic protocols remain strikingly limited. In particular, despite the rising emergence of immunotherapy as a promising cancer treatment, knowledge gained from mathematical modeling of tumorimmune interactions often still eludes application to the clinic. The currently underutilized potential of such techniques to forecast response to treatment, aid the development of immunotherapeutic regimes and ultimately streamline the transition from innovative concept to clinical practice is hence the focus of this review.
Mathematical oncologyDue to the simplifications inherent in the development of a mathematical model of a complex biological system, early attempts at combining mathematics with biology were often met with skepticism from experimentalists and clinicians. The misconception that simplifications render mathematical models meaningless is still found in some more conservative areas of medical research. Thankfully, the great potential for theoretical models to help unravel highly complex and multifaceted processes without the need for . CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/027979 doi: bioRxiv preprint first posted online 2 time-consuming experimentation is becoming more widely appreciated [4]. Insights can be gained into mechanisms or relationships that may not be obvious or intuitive, allowing the generation of novel hypotheses on which to base future experimentation.Formalized descriptions of dynamic processes that have achieved a balance of both simplicity and applicability have contributed greatly to biological research to date. For example, in the field of oncology, tumor growth has been modeled extensively using methods ranging from simple one-equation models featuring logistic, Gompertz or exponential growth functions to detailed 3-dimensional spatio-temporal systems [5][6][7][8][9][10][11][12][13][14][15]. Detailed reviews of tumor growth modeling over the last few decades are...