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Mathematics
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Modelling and Control in Healthcare and Biology
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Modelling and Control in Healthcare and Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (20 January 2023) | Viewed by 7820

Special Issue Editors

Prof. Dr. Eva H. Dulf

E-Mail Website
Guest Editor
1. Faculty of Automation and Computer Science, Department of Automation, Technical University of Cluj-Napoca, Memorandumului 28, 400014 Cluj-Napoca, Romania
2. Physiological Controls Research Center, Obuda University, 1034 Budapest, Hungary
Interests: fractional calculus; control engineering; biochemical engineering; biomedical engineering
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Levente Kovács

E-Mail Website
Guest Editor
Physiological Controls Research Center, Research, Innovation and Service Center, Òbuda University, 1034 Budapest, Hungary
Interests: physiological modeling and control; modern robust control theory; cyber-medical systems; biomedical engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Interdisciplinary approach of research topics is becoming an increasing need in scientific communities. The strong interconnection between applied mathematics and biomedical sciences/engineering asks for such an approach. Mathematical modeling is a vital research tool to explore complex systems from medical applications. Data-driven approaches to health outcome assessment, artificial intelligence, and mathematical, computational, methodological, and technological advances are the core of effective healthcare system management. The application of signal and image processing techniques has played a vital role in assisting surgeons and physicians in diagnosing diseases and performing surgeries on patients. Clinical medical devices have erupted through a combination of applied mathematics techniques, which represent a giant leap in the medical field. Artificial intelligence has the capability of detecting meaningful relationships in a data set and has been widely used in many clinical situations to diagnose, treat, and predict results.

We cordially invite researchers to contribute original research articles as well as review articles that will promote the development of new approaches for medical applications. With this Special Issue, we hope to stimulate continuing efforts to solve real-world medical problems with advanced theories and technologies of applied mathematics as well as provide a good opportunity for researchers in applied mathematics, medical sciences, and engineering fields to discuss the current state-of-the-art knowledge of this emerging interdisciplinary research field. Potential topics include but are not limited to:

  • Mathematical modeling in medicine;
  • Optimization techniques in medicine;
  • Neural networks in medicine;
  • Biomedical signal and image processing;
  • Physiological feedback control;
  • Applied statistics in medicine.

Prof. Dr. Eva H. Dulf
Prof. Dr. Levente Kovács
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

  • modeling
  • optimization
  • artificial intelligence
  • control theory

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Published Papers (4 papers)

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Research

17 pages, 1626 KiB  
Article
Validation of a Probabilistic Prediction Model for Patients with Type 1 Diabetes Using Compositional Data Analysis
by Alvis Cabrera, Lyvia Biagi, Aleix Beneyto, Ernesto Estremera, Iván Contreras, Marga Giménez, Ignacio Conget, Jorge Bondia, Josep Antoni Martín-Fernández and Josep Vehí
Mathematics 2023, 11(5), 1241; https://doi.org/10.3390/math11051241 - 4 Mar 2023
Cited by 1 | Viewed by 1566
Abstract
Glycemia assessment in people with type 1 diabetes (T1D) has focused on the time spent in different glucose ranges. As this time reflects the relative contributions to the finite duration of a day, it should be treated as compositional data (CoDa) that can [...] Read more.
Glycemia assessment in people with type 1 diabetes (T1D) has focused on the time spent in different glucose ranges. As this time reflects the relative contributions to the finite duration of a day, it should be treated as compositional data (CoDa) that can be applied to T1D data. Previous works presented a tool for the individual categorization of days and proposed a probabilistic transition model between categories, although validation has hitherto not been presented. In this study, we consider data from eight real adult patients with T1D obtained from continuous glucose monitoring (CGM) sensors and introduce a methodology based on compositional methods to validate the previously presented probability transition model. We conducted 5-fold cross-validation, with both the training and validation data being CoDa vectors, which requires developing new performance metrics. We design new accuracy and precision measures based on statistical error calculations. The results show that the precision for the entire model is higher than 95% in all patients. The use of a probabilistic transition model can help doctors and patients in diabetes treatment management and decision-making. Although the proposed method was tested with CoDa applied to T1D data obtained from CGM, the newly developed accuracy and precision measures apply to any other data or validation based on CoDa. Full article
(This article belongs to the Special Issue Modelling and Control in Healthcare and Biology)
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21 pages, 2953 KiB  
Article
Proof of Concept Control of a T1DM Model Using Robust Fixed-Point Transformations via Sliding Mode Differentiators
by Bence Czakó, Dániel András Drexler and Levente Kovács
Mathematics 2023, 11(5), 1210; https://doi.org/10.3390/math11051210 - 1 Mar 2023
Viewed by 1257
Abstract
Type 1 Diabetes Mellitus (T1DM) is a disease where insulin production is obstructed in the pancreas, and exogenous administration of the hormone must be utilized. Automatic control of the administration can be achieved using the Artificial Pancreas (AP) concept, whose performance is heavily [...] Read more.
Type 1 Diabetes Mellitus (T1DM) is a disease where insulin production is obstructed in the pancreas, and exogenous administration of the hormone must be utilized. Automatic control of the administration can be achieved using the Artificial Pancreas (AP) concept, whose performance is heavily reliant on the underlying control algorithm. A Robust Fixed-Point Transformations (RFPT)-based control strategy was designed to automate the insulin delivery process, which incorporates a Sliding Mode Differentiator (SMD) to provide higher order derivatives of the blood glucose level. Inter-patient variability, carbohydrate disturbances, and real-life sampling were included in the validation of the method. Results showed that the algorithm could regulate the blood glucose level, with a significant overshoot at the beginning of the control action due to the adaptive nature of the controller. Results indicate that the design requires additional modifications to be feasible in practice, including an extended validation with more virtual patients and realistic simulation settings in the future. Nevertheless, the current control algorithm has several attractive features, which are discussed with respect to PID and Model Predictive Control (MPC). Full article
(This article belongs to the Special Issue Modelling and Control in Healthcare and Biology)
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27 pages, 1102 KiB  
Article
Analyzing an Epidemic of Human Infections with Two Strains of Zoonotic Virus
by Yongxue Chen, Hui Zhang, Jingyu Wang, Cheng Li, Ning Yi and Yongxian Wen
Mathematics 2022, 10(7), 1037; https://doi.org/10.3390/math10071037 - 24 Mar 2022
Cited by 3 | Viewed by 1706
Abstract
Due to the existence and variation of various viruses, an epidemic in which different strains spread at the same time will occur. here, an avian–human epidemic model with two strain viruses are established and analyzed. Both theoretical and simulation results reveal that the [...] Read more.
Due to the existence and variation of various viruses, an epidemic in which different strains spread at the same time will occur. here, an avian–human epidemic model with two strain viruses are established and analyzed. Both theoretical and simulation results reveal that the mixed infections intensify the epidemic and the dynamics become more complex and sensitive. There are six equilibria. The trivial equilibrium point is a high-order singular point and will undergo the transcritical bifurcations to bifurcate three equilibria. The existence and stability of equilibria mainly depend on five thresholds. A bifurcation portrait for the existence and stability of equilibria is presented. Simulations suggest that the key control measure is to develop the identification technology to eliminate the poultry infected with a high pathogenic virus preferentially, then the infected poultry with a low pathogenic virus in the recruitment and on farms. Controlling contact between human and poultry can effectively restrain the epidemic and controlling contagions in poultry can avoid great infection in humans. Full article
(This article belongs to the Special Issue Modelling and Control in Healthcare and Biology)
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12 pages, 2646 KiB  
Article
A Model of Optimal Interval for Anti-Mosquito Campaign Based on Stochastic Process
by Bingyin Lei, Kaiye Gao, Li Yang and Shu Fang
Mathematics 2022, 10(3), 440; https://doi.org/10.3390/math10030440 - 29 Jan 2022
Cited by 1 | Viewed by 2048
Abstract
Mosquito control is very important, in particular, for tropical countries. The purpose of mosquito control is to decrease the number of mosquitos such that the mosquitos transmitted diseases can be reduced. However, mosquito control can be costly, thus there is a trade-off between [...] Read more.
Mosquito control is very important, in particular, for tropical countries. The purpose of mosquito control is to decrease the number of mosquitos such that the mosquitos transmitted diseases can be reduced. However, mosquito control can be costly, thus there is a trade-off between the cost for mosquito control and the cost for mosquitos transmitted diseases. A model is proposed based on renewal theory in this paper to describe the process of mosquitos’ growth, with consideration of the mosquitos transmitted diseases growth process and the corresponding diseases treatment cost. Through this model, the total mosquitos control cost of different strategies can be estimated. The optimal mosquito control strategy that minimizes the expected total cost is studied. A numerical example and corresponding sensitivity analyses are proposed to illustrate the applications. Full article
(This article belongs to the Special Issue Modelling and Control in Healthcare and Biology)
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