Mathematical biology has been an area of wide interest in recent decades, since the modeling of complicated biological processes became able to create analytical and computational approaches for many different bio-inspired problems, coming from different branches such as population dynamics, molecular dynamics in cells, neuronal and heart diseases, the cardiovascular system, genetics, etc. Mathematical and computer sciences have come to work interactively to contribute to a better understanding of biological phenomena.

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. 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.

This Special Issue welcomes original research and review articles on insightful approaches to treat the basic relationships between species in population dynamics and implementation of species interactions in complex networks to model natural ecosystems. Furthermore, any other kind of models and their applications in neuroscience, genetics, cellular and molecular dynamics, heart diseases, etc., and where the fusion of mathematics and computation helps progress in biological problems are also welcome.

Potential topics include but are not limited to the following:

• Categorical and indicational models of the causality of biological organization
• Modeling relation between autopoietic and (M,R) systems
• Formal and causal differences between biological and non-biological systems
• Optimization and machine learning algorithms for biomedical data
• Mathematical, computational, biophysical, and statistical modeling
• Expert systems in medicine and non-algorithmic mathematical models
• Cognition, autonomy, anticipation, and self-reference in the causal organization of biological systems
• Calculus of indications, algebraic biology, self-reference, and heart disease modeling