Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development.