What field integrates mathematical models with biological processes?

Mathematical biology is the field that specifically focuses on the development and application of mathematical models to understand biological processes. This integration allows researchers to quantify and predict biological behaviors and interactions, ranging from population dynamics and epidemiology to the spread of diseases and the modeling of ecological systems. By using mathematical equations and simulations, scientists can analyze complex biological phenomena and derive insights that might be difficult to obtain through empirical data alone.

In contrast to the other fields mentioned, mathematical biology is distinct in its heavy reliance on mathematical principles and techniques to address and solve biological problems. Qualitative biology involves understanding biological systems through descriptive methods rather than quantitative modeling. Theoretical biology encompasses broad theoretical frameworks that may not always include a mathematical component, while statistical biology focuses more on the application of statistics to biological data rather than the creation of models that represent biological processes through mathematics. Thus, mathematical biology plays a crucial role in bridging mathematics with biological study, making it the correct answer.