Mathematical Modeling and Analysis in Biology and Medicine

Dear Colleagues,

Over the recent decades, mathematical models have been actively used in various fields of technology and science, both in the natural and in the social sciences.

An important domain of their application is the mathematical modeling of complex systems, and in particular living systems. Real experiments in some cases cannot be conducted on living beings due to the complexity of their organisms or due to the lack of necessary technology in some situations. Such experiments are often long-lasting, expensive, and problematic from an ethical viewpoint.

Mathematical models can describe some characteristic properties of the phenomena under consideration and predict the possible scenarios for their course without the need to conduct real experiments.

Unlike the modeling of physicomechanical systems, scientists dealing with biological systems need to consider the specific differences between living and inert matter. As is well known, systems pertaining to inert matter can be described using invariance principles and conservation laws, and the interactions between their individual elements follow the laws of classical or quantum mechanics. In contrast, in living organisms, these laws cannot be directly applied. Because of their nature and the need to survive, living beings are characterized by high internal complexity. They eat, breathe, protect themselves from pests and predators, and as a result, complex processes of transformation of substances and energy take place.

In the process of centuries of evolution, in their struggle for survival in a variety of conditions, organisms have improved themselves, developing the ability to change the ways of functioning of their constituting elements, and eventually their reproduction or destruction depending on the respective conditions.

Mathematical models have been successfully applied to study various diseases, such as cancer, infectious, autoimmune, cardiovascular, neurodegenerative, and others. The topic is especially relevant in view of the development of COVID‑19.

Mathematical modeling can contribute to the improvement of understanding the role of key factors in various biological processes and phenomena—in particular, the occurrence and development of various diseases in medicine, the improvement of existing and creation of new drugs, the optimization of treatment protocols, and the improvement of hospital technology and effective healthcare system management. The proposed applications of models in biology and medicine can impact the development of mathematical theory and computational methods.

The purpose of this Special Issue is to publish qualitative papers, referring but not limited to the derivation of new and improvement of existing mathematical models, designed at various observation and representation scales, applicable in biology and medicine, their qualitative and quantitative analysis, as well as comparison of the results of the modeling with experimental and clinical data.

Please note that all of the submitted papers must be within the general scope of the Mathematics journal.

Dr. Mikhail Kolev
Guest Editor

Manuscript Submission Information

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