Preface to Special Issue “Mathematical Modeling and Data Science for Biology and Medicine”

This Special Issue, titled “Mathematical Modeling and Data Science for Biology and Medicine”, aims to highlight the development and growing application of mathematical models and data science in medicine, as well as their role in enhancing the understanding and clinical management of various diseases. The ten articles included in this Issue explore a diverse array of topics, such as cell differentiation, blood flow, tumor growth under virotherapy, chemotherapy treatment sequences for triple-negative locally advanced breast cancer, incidence-dependent management strategies against an SEIRS epidemic, important measures for the prevention and control of the COVID-19 epidemic, invadopodia formation in cancer cells, fitting parameters for multi-exponential diffusion-weighted MRI, and oncolytic virotherapy. These studies employ a variety of mathematical tools, including graph theory, transport equation, systems of ordinary differential equations, systems of nonlinear diffusion equations, free boundary problems, center manifold theory, and optimization techniques, to model a wide range of biological processes. In addition, medical applications are presented based on their mathematical analyses and numerical simulations. Through these articles, readers will gain valuable insight into the latest trends and applications of mathematical modeling in medicine.

The first contribution introduces a similarity network-based approach to investigate the role of interacting single-cell histone modifications. High-resolution peak counting is shown to be an effective method for constructing per-gene profiles of histone modification marks. The second contribution focuses on the theoretical analysis of the effects of boundary conditions on the solutions of a one-dimensional hemodynamic system. The author extends the applicability of analytical methods in the simulation of blood flow, highlighting the influence of boundary conditions. The third contribution presents a mathematical model, based on ordinary differential equations, to examine the spatially homogenous state of tumor growth under virotherapy. Derived from a partial differential equation (PDE) system, the model is used to analyze the time evolution of the tumor radius and its implications for tumor progression. The fourth contribution studies triple-negative locally advanced breast cancer and underscores the regions exhibiting the most sustained variation in the tumor’s cellular population. The fifth contribution showcases a model for the prevention and control of COVID-19, integrating healthcare and medical detection with big data information technology to monitor epidemic trends throughout the entire course of the outbreak. The sixth contribution introduces a mathematical model of an individual cell to simulate invadopodia formation in a three-dimensional domain. The model is formulated using the Stefan problem approach, where the free boundary of the membrane is determined. The subsequent contribution develops a mathematical model to study the impact of epidemic dynamics on non-pharmaceutical interventions. Specifically, an SEIRS epidemic model with reinfection is used to illustrate the results, with an application to the COVID-19 pandemic. The eighth contribution examines the airborne and physical transmission of COVID-19 within a simple heuristic framework designed to inform public policy decisions. The ninth contribution utilizes diffusion-weighted MRI and compares different methods for multi-exponential analysis of the diffusion signal in the kidneys. The final contribution explores the impact of Allee effects on tumor cell growth through the mathematical modeling of oncological virotherapy. The authors employ an epidemiological model integrating linear and logistic growth, applying different Allee effects to observe their influence on the dynamics of virus–tumor interaction.

The Guest Editor extends his sincere appreciation to all the authors for their valuable contributions to this Special Issue. He is also deeply grateful to the reviewers for their insightful and professional evaluation reports, which have significantly enhanced the quality of the submitted manuscripts. Furthermore, he acknowledges the excellent collaboration with the publisher, the outstanding assistance of the MDPI associate editors, and the significant support of the Managing Editor of this Special Issue, Ms. Helene Hu.