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Mathematics
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Modeling, Identification and Control of Biological Systems
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Modeling, Identification and Control of Biological Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 20 February 2026 | Viewed by 2006

Special Issue Editors

Dr. Alessandro Borri

E-Mail Website
Guest Editor
Institute for Systems Analysis and Computer Science “A. Ruberti”, National Research Council, 19 00185 Rome, Italy
Interests: applied mathematics; hybrid systems; digital control; systems biology; biomathematics; control applications
Dr. Federico Papa

E-Mail Website
Guest Editor
Institute for Systems Analysis and Computer Science “A. Ruberti”, National Research Council, 19 00185 Rome, Italy
Interests: mathematical modeling of biological systems; modeling and control of tumor growth and treatment; modeling and control of epidemics; systems biology; mathematical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Applied mathematics enables the transformation of available real-world data and observations into mathematical structures and theoretical concepts. The obtained mathematical models are powerful investigation instruments for exploring the underlying principles of real systems and for tackling open problems in the natural sciences, particularly in physics, biology, and medicine. These models are valuable descriptive tools that shed light on the inner mechanisms of intricate biological systems. They also offer reliable predictions about the future behavior of the real systems and their responses to various external stimuli. Additionally, the control theory equips researchers with the essential tools to design effective, sometimes optimal, inputs for managing the behavior of these models. This aspect allows scientists to support decision-makers in devising intervention strategies for the management of emergencies in public health and for the treatment of pathological conditions in medicine.

The increasing volume of scholarly articles on mathematical modeling and control in biology serves as strong evidence of the growing influence of this research field on biomedicine and public health. This Special Issue is dedicated to gathering innovative contributions from experienced researchers in the realm of mathematical modeling and control theory as applied to biology and medicine. We welcome original research papers and reviews.

Dr. Alessandro Borri
Dr. Federico Papa
Guest Editors

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

  • mathematical modeling of biological systems
  • mathematical physics
  • computational biology and medicine
  • system identification and filtering
  • optimal control and game theory
  • systems biology
  • dynamical systems
  • mathematical oncology
  • epidemic modeling
  • structured population models
  • biochemical networks

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Published Papers (3 papers)

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20 pages, 2625 KiB  
Article
Temperature-Dependent Kinetic Modeling of Nitrogen-Limited Batch Fermentation by Yeast Species
by Artai R. Moimenta, Romain Minebois, David Henriques, Amparo Querol and Eva Balsa-Canto
Mathematics 2025, 13(9), 1373; https://doi.org/10.3390/math13091373 - 23 Apr 2025
Viewed by 250
Abstract
Yeast batch fermentation is widely used in industrial biotechnology, yet its performance is strongly influenced by temperature and nitrogen availability, which affect growth kinetics and metabolite production. The development of predictive models that accurately describe these effects is essential for automating and optimizing [...] Read more.
Yeast batch fermentation is widely used in industrial biotechnology, yet its performance is strongly influenced by temperature and nitrogen availability, which affect growth kinetics and metabolite production. The development of predictive models that accurately describe these effects is essential for automating and optimizing fermentation design, reducing trial-and-error experimentation, and improving process efficiency and product quality. However, most mathematical models focus on primary metabolism and lack a systematic approach to integrate the effects of temperature. Existing models often rely on empirical corrections with limited predictive power beyond specific experimental conditions. Furthermore, there is no unified framework for optimizing fermentation processes while accounting for the temperature-dependent metabolic responses. We addressed these gaps by developing a temperature-dependent kinetic model for nitrogen-limited batch fermentation by Saccharomyces cerevisiae. The modeling approach is based on advanced systems identification, integrating identifiability analyses (structural and practical), multi-experiment parameter estimation, and automated model selection to determine the most appropriate temperature dependencies for key metabolic processes. Validated across five industrial S. cerevisiae strains in an illustrative example related to wine fermentation, the model exhibited strong predictive performance (NRMSE <10.5%, median R2>0.95) and enabled simulation-based process optimization, including nitrogen-supplementation strategies and strain selection for improved fermentation outcomes. By providing a systematic modeling framework that accounts for temperature effects, this work bridges a critical gap in predictive modeling and advances the rational design and control of industrial fermentation processes. Full article
(This article belongs to the Special Issue Modeling, Identification and Control of Biological Systems)
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23 pages, 1571 KiB  
Article
The Memory Lag Regulates the Threshold Effect Within the Repressor Gene Module
by Fengquan Chen, Sizhe Wang, Shan Li and Haohua Wang
Mathematics 2025, 13(7), 1154; https://doi.org/10.3390/math13071154 - 31 Mar 2025
Viewed by 181
Abstract
The abundance level of the lambda phage repressor is randomly fluctuated by the influence of multiple ligand signals, inducing its phenotypic diversity. However, the mechanism of how the memory lag of fluctuations and the nonlinear structure of the expression system regulate the phenotypic [...] Read more.
The abundance level of the lambda phage repressor is randomly fluctuated by the influence of multiple ligand signals, inducing its phenotypic diversity. However, the mechanism of how the memory lag of fluctuations and the nonlinear structure of the expression system regulate the phenotypic diversity is still obscure. Here, we try to investigate a prototypical regulatory network coupled with random fluctuations (noise) and nonlinear structures to focus on the impact of protein abundance fluctuations within bacteriophages on cellular phenotypic transitions and energy dissipation throughout the process. Our findings reveal that there exists a threshold of the CI protein abundance to regulate the switching from the lysogenic to lytic states of the lambda phage, influencing its reproductive strategy. Specifically, an increase in the memory lag of multiplicative noise leads to a delayed transition from the lysogenic to lytic states. Additive noise exerts an effect that is nearly the opposite of that of multiplicative noise. Furthermore, we reconstruct the effective equivalent topological network to calculate the energy consumption cost of these switching. It is indicated that it only dissipates the lower energy to achieve the bimodality in a low-noise environment. In contrast, it needs to dissipate more energy to maintain the stability of the expression system in larger fluctuations. Comprehensive analysis suggests that lambda phages can optimize their survival strategies by modulating the cellular microenvironment, specifically through adjusting noise intensity and memory lag. Full article
(This article belongs to the Special Issue Modeling, Identification and Control of Biological Systems)
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15 pages, 2634 KiB  
Article
Optimal Control Strategies for Dengue and Malaria Co-Infection Disease Model
by Muhammad Imran, Brett Allen McKinney, Azhar Iqbal Kashif Butt, Pasquale Palumbo, Saira Batool and Hassan Aftab
Mathematics 2025, 13(1), 43; https://doi.org/10.3390/math13010043 - 26 Dec 2024
Cited by 1 | Viewed by 1053
Abstract
Dengue and malaria fever infections are mosquito-borne diseases that pose significant threats to human health. There is an urgent need for effective strategies to prevent, control, and raise awareness about the public health risks of dengue and malaria. In this manuscript, we analyze [...] Read more.
Dengue and malaria fever infections are mosquito-borne diseases that pose significant threats to human health. There is an urgent need for effective strategies to prevent, control, and raise awareness about the public health risks of dengue and malaria. In this manuscript, we analyze a mathematical model that addresses the dynamics of dengue–malaria co-infection and propose optimal control strategies across four different scenarios to limit the spread of the disease. The results indicate that non-pharmaceutical interventions are the most effective and feasible standalone strategy, yielding significant reductions in disease transmission. Additionally, vector population control through spraying is identified as the second most significant method, with a proportional decrease in disease prevalence corresponding to the reduction in the mosquito population. While pharmaceutical treatments alone do not fully eradicate the disease, they do contribute to its containment. Notably, the combination of vector control and non-pharmaceutical strategies proved to be the most effective approach, ensuring rapid disease eradication. These findings emphasize the importance of integrated interventions in managing co-infection dynamics and highlight the vital role of prevention-oriented strategies. Full article
(This article belongs to the Special Issue Modeling, Identification and Control of Biological Systems)
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