Mathematical and Computational Modeling in Biology and Medicine
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".
Deadline for manuscript submissions: 31 October 2026 | Viewed by 2
Special Issue Editor
2. Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54 Street, 10-710 Olsztyn, Poland
Interests: mathematical modeling; numerical methods; statistical analysis; linear regression; machine learning; programming; biology
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
In recent decades, mathematical models have been actively used in various fields of technology and science, including both the natural and social sciences.
An important domain of their application is the mathematical modeling of complex systems, particularly living systems. Real experiments in some cases cannot be conducted on living beings due to the complexity of their organisms or the lack of necessary technology. 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 matters. 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.
Through centuries of evolution, in their struggle for survival under diverse conditions, organisms have developed the ability to modify the functioning of their constituent elements, and, ultimately, to regulate their own reproduction or destruction in response to environmental changes.
Mathematical models have been successfully applied to the study of various diseases, such as cancer, infectious, autoimmune, cardiovascular, and neurodegenerative disorders.
While physiologically based models provide a solid framework for simulating complex interactions, they are fundamentally constrained by deterministic equations with fixed parameters. In real clinical settings, however, various stochastic factors—such as unrecorded meal compositions, fluctuations in physical activity, hormonal changes, and sensor inaccuracies—can play a significant role. These unpredictable elements introduce variability that purely mechanistic models struggle to accommodate, leading to discrepancies between predicted and actual biochemical patterns observed in everyday life.
Machine learning serves as a valuable enhancement to traditional simulation methods by identifying patterns directly from data, allowing models to adjust to individual behaviors and environmental factors. Machine learning algorithms excel at capturing nonlinear relationships, correcting model errors, and estimating hidden variables not explicitly represented in physiological models. When combined with stochastic simulation, machine learning components can enhance forecasting precision, adapt to new inputs, and assess prediction uncertainty.
Mathematical and computational 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 high-quality papers focused on the derivation of new and improvement of existing mathematical and computational models designed at various observational and representational scales. These models should be applicable to biology and medicine and include both qualitative and quantitative analyses, as well as comparisons between modeling results and experimental or clinical data.
Please note that all submitted papers must be within the general scope of Mathematics.
Dr. Mikhail Kolev
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- deterministic models
- stochastic models
- discrete models
- continuous models
- multiscale models
- population models
- epidemic models
- kinetic models
- active particles
- machine learning
- models with delay
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