Mathematical Modelling of Cancer across Scales: A Topical Collection in Celebration of Mark Chaplain's 60th Birthday

Mathematical models have played an increasingly prominent role in cancer research as tools to consolidate experimental and clinical data, dissect out biological processes, provide a formal basis for the formulation of novel hypotheses, inform new experiments that may help identify unexplored research streams, and suggest novel treatment strategies. Developing mathematical models for multifaceted processes such as those implicated in cancer dynamics, which involve a plurality of interdependent mechanisms that dynamically interact over a wide range of spatio-temporal scales, entails harnessing methods and techniques from across different areas of the mathematical sciences. This is exemplified by the ground-breaking research of Mark Chaplain, whose contributions in the mathematical modelling of tumour growth and treatment have been highly influential on the development of mathematical oncology into a research area in its own right within the field of mathematical biology. Mark Chaplain's research contributions comprise a variety of multiscale mathematical models – including continuum models formulated as nonlinear ordinary and partial differential equations, discrete (i.e. individual-based) models, and hybrid discrete-continuum models – for a broad spectrum of subcellular, cellular, and tissue-scale phenomena – encompassing avascular tumour growth, the immune response to cancer, tumour-induced angiogenesis, vascular tumour growth, invasion and metastasis – which have built an ongoing legacy of innovation in mathematical biology, in general, and mathematical oncology, in particular. This topical collection will celebrate Mark Chaplain's 60th birthday by bringing together a series of articles on recent advances in the development and study of continuum, discrete, and hybrid discrete-continuum models for the intra-cellular and cellular processes, as well as the interactions between cells and the extra-cellular environment, that are at the root of cancer onset and progression *Invitation only collection*