Abstract

Mathematical modeling is a technique that is increasingly the preferred choice for the current era of biology, where the researcher catches a glimpse of the underlying biological processes using precise, quantitative modeling approaches. This paper provides a current update on the progress that is unfolding within the realm of numerical optimization for biological modeling, and the new computer-based approaches that are transforming the landscape for the better. It provides a perspective on the history of the development of biological modeling approaches that evolved sequentially, initially through very elementary, deterministic approaches, progressively advancing to increasingly complex approaches that are stochastic and multi-scale, the current advances that are emerging using new approaches for the improvement of model parameter estimation, comparison, and forecasting, the connection between machine learning and biological modeling, the development of new hybrid modeling approaches, and the challenges that emerge forth with large-scale biological data.