Modeling and quantitative analysis stand as indispensable tools in medicine, offering invaluable insights, predictive capabilities, and actionable solutions to address a myriad of healthcare challenges. Their instrumental role in advancing our understanding of disease dynamics has paved the way for enhanced diagnosis, prognosis, and treatment capabilities. This dissertation showcases the pivotal role of modeling methods and quantitative analysis in medicine, presented through three distinct applications that span over advanced drug delivery systems, cancer prognosis and the evolution of chemoresistance. In the first part of this work, a comprehensive mathematical model of transdermal drug delivery via microneedle-based patches, integrated with a pharmacokinetics model, is introduced. Model-based simulations were conducted to pinpoint the key parameters governing systemic delivery, enabling the optimization of patch designs to improve drug pharmacokinetics. In the second part, survival analysis is employed to identify biomechanical and immune biomarkers, enabling the prospective prediction of tumor aggressiveness, invasiveness, treatment outcomes, and survival probability in breast cancer. Lastly, a novel hypothesis is presented, proposing that water exclusion zones within cells may act as insulation barriers, safeguarding the delicate quantum nature of specific biochemical reactions against environmental influences. This hypothesis gains additional support through a review regarding the role that interfacial water plays in several biological processes and a proof of concept example to illustrate the application of quantum mechanics models for understanding the evolution of chemoresistance. Through these multifaceted investigations, this dissertation underscores the vital role that modeling and quantitative analysis plays in investigating the complexities of diseases, promising new horizons in medicine.