Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure toward drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review we discuss the promising opportunities that these interdisciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.

癌症是一个克隆进化过程。鉴于对耐药性的持续选择压力，这为有效的治疗干预提出了挑战。从种群遗传学，进化动力学和工程学角度的数学建模正越来越多地用于研究肿瘤进展，肿瘤内异质性，耐药性以及合理的药物调度和组合设计。在这篇综述中，我们讨论了这些跨学科方法为癌症生物学和治疗进展所带来的有希望的机会。我们建议定量建模的观点可以补充新兴的实验技术，以促进对疾病进展的了解和治疗药物方案设计的提高的能力。