Applied mathematics and nonlinear sciences in the war on cancer

Abstract

Cancer is a major health problem in the industrialized world being the second leading cause of death in the USA and EU after heart disease. A huge quantity of resources is spent every year on cancer research, resulting in a small, yet sustained, reduction in cancer death rates (in the last ten years this was about 1 − 2% per year in the US) [1]. However, there is a widespread concern about the slow pace at which these discoveries in fundamental biology are translated into safe and effective clinical interventions. Statistics is already considered to be a basic ingredient of medical education and routinely used in research, specifically in clinical studies. This is so even when many physicians have a limited understanding of statistics and risk analysis [2]. However, the potential of other mathematical tools such as differential equations, advanced numerical methods, optimization, etc, have not been broadly incorporated into medical research on clinical care. This is so in spite of the fact that these methods are part of the standard toolbox of the applied mathematician that have proven useful in many other fields of science and engineering.