Grand challenges in mathematical biology: Integrating multi-scale modeling and data

Despite the fact that mathematical applications to biology and medicine have been mentioned since the eighteenth century [1] [or even earlier, if we think of Fibonacci's example of a rabbit population growth [2]], the evolution of this research field was slow until the twentieth century. Unlike mathematical applications to physical problems (where equations can describe accurately the physical reality), applications to biological problems are much more complex due to the evolutionary nature of the living matter [3, 4]. Moreover, this evolution of biological systems occurs on different spatial and temporal scales (see Figure 1), which renders the modeling much more challenging. Also, the mathematical and statistical investigation of these multi-scale models is more challenging, due to the complexities of the interactions between the scales.