Journal articles: 'Medicine – Mathematical models'

1

Knapp, David, and Richard Bellman. "Mathematical Models in Medicine." Mathematical Gazette 70, no. 451 (March 1986): 79. http://dx.doi.org/10.2307/3615870.

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Zietz, Stanley. "Computers and Mathematical Models in Medicine." Mathematical Biosciences 75, no. 1 (July 1985): 139–40. http://dx.doi.org/10.1016/0025-5564(85)90070-7.

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Lyshchuk, V. A., D. A. Andrikov, D. SH Hazizova, O. V. Drakina, S. V. Kalyn, L. V. Sazykina, and H. V. Shevchenka. "Methods of mathematical medicine." Electronics and Communications 16, no. 3 (March 28, 2011): 176–80. http://dx.doi.org/10.20535/2312-1807.2011.16.3.266442.

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The decision of the main problem for development of mathematical medicine – definitions of criteria and restrictions for synthesis and therapy optimization is proposed. The methods described here connected to elaboration of the mathematical models, control of medical treatment, individualization and use of models, allocation of pathological processes. The separation of pathological and adaptive organism reactions (homeostatic, compensatory, protective) wasn’t realized early. Methods give the possibiliy to estimate numericaly efficiency and helpfully of medicinal therapy, and also the quality of treatment. On the basis of these methods the technologies provided physicians decision of doctor have been carrying out. This technologies were successfully applied in treatment of more than 4000 serious patients

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4

Jódar, Lucas, Luis Acedo, and Juan Carlos Cortés. "Mathematical models in medicine, business and engineering 2009." Mathematical and Computer Modelling 52, no. 7-8 (October 2010): 947–48. http://dx.doi.org/10.1016/j.mcm.2010.03.033.

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5

Adomian, George. "Solving the mathematical models of neurosciences and medicine." Mathematics and Computers in Simulation 40, no. 1-2 (December 1995): 107–14. http://dx.doi.org/10.1016/0378-4754(95)00021-8.

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Kozhanov, V. S., S. O. Ustalkov, and A. O. Khudoshina. "TOW CABLES MATHEMATICAL MODELS." Mathematical Methods in Technologies and Technics, no. 5 (2022): 62–68. http://dx.doi.org/10.52348/2712-8873_mmtt_2022_5_62.

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Scherer, Almut, and Angela McLean. "Mathematical models of vaccination." British Medical Bulletin 62, no. 1 (July 1, 2002): 187–99. http://dx.doi.org/10.1093/bmb/62.1.187.

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8

Nikolova, Iveta. "On stochastic models in biology and medicine." Asian-European Journal of Mathematics 13, no. 08 (May 21, 2020): 2050168. http://dx.doi.org/10.1142/s1793557120501685.

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Stochastic models along with deterministic models are successfully used for mathematical description of biological processes. They apply knowledge from probability theory and mathematical statistics to analyze specific characteristics of living systems. The paper is devoted to some stochastic models of various phenomena in biology and medicine. Basic concepts and definitions used in classical probability models are considered and illustrated by several examples with solutions. The stochastic kinetic modeling approach is described. A new kinetic model of autoimmune disease is presented. It is a system of nonlinear partial integro-differential equations supplemented by corresponding initial conditions. The modeling problem is solved computationally.

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Dauhoo, Muhammad Zaid, Laurent Dumas, and Pierre Gabriel. "CIMPA School on Mathematical Models in Biology and Medicine." ESAIM: Proceedings and Surveys 62 (2018): I. http://dx.doi.org/10.1051/proc/201862000.

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Krylov, A. P. "Mathematical modeling in modern medicine. Fields. Approaches. Problems." Terapevt (General Physician), no. 9 (August 15, 2020): 75–79. http://dx.doi.org/10.33920/med-12-2009-08.

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Calderale, P. M., and G. Scelfo. "Mathematical Models of Musculoskeletal Systems." Engineering in Medicine 16, no. 3 (July 1987): 131–46. http://dx.doi.org/10.1243/emed_jour_1987_016_032_02.

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An understanding of the forces which act in the musculo-skeletal system is required in a number of applications. This study provides a critical and comparative discussion of the methods used to determine the muscle and joint forces, and presents an analysis of future prospects for applying these methods.

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12

Eggermont, J. J. "Mathematical Models for Developmental Changes." Acta Oto-Laryngologica 99, sup421 (January 1985): 102–7. http://dx.doi.org/10.3109/00016488509121763.

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13

Thompson, R. Paul. "Causality, mathematical models and statistical association: dismantling evidence-based medicine." Journal of Evaluation in Clinical Practice 16, no. 2 (March 30, 2010): 267–75. http://dx.doi.org/10.1111/j.1365-2753.2010.01383.x.

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Anissimov, Yuri G. "Mathematical models for skin toxicology." Expert Opinion on Drug Metabolism & Toxicology 10, no. 4 (February 4, 2014): 551–60. http://dx.doi.org/10.1517/17425255.2014.882318.

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15

Schneider, B., and G. I. Marchuk. "Mathematical Models in Immunology." Biometrics 42, no. 4 (December 1986): 1003. http://dx.doi.org/10.2307/2530721.

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16

Flaherty, Brendan, J. P. McGarry, and P. E. McHugh. "Mathematical Models of Cell Motility." Cell Biochemistry and Biophysics 49, no. 1 (July 25, 2007): 14–28. http://dx.doi.org/10.1007/s12013-007-0045-2.

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17

Coronel, Ruben. "Myths, metaphors, and mathematical models." Heart Rhythm 4, no. 8 (August 2007): 1046–47. http://dx.doi.org/10.1016/j.hrthm.2007.05.015.

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18

Anderson, Russell W. "Mathematical models of HIV pathogenesis." Nature Medicine 3, no. 9 (September 1997): 936. http://dx.doi.org/10.1038/nm0997-936a.

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19

Grossman, Zvi, and Ronald B. Herberman. "Mathematical models of HIV pathogenesis." Nature Medicine 3, no. 9 (September 1997): 936–37. http://dx.doi.org/10.1038/nm0997-936b.

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20

Thames, Howard. "Mathematical Models in Cancer Research." International Journal of Radiation Biology 57, no. 5 (January 1990): 1063. http://dx.doi.org/10.1080/09553009014551161.

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21

Castillo-Chavez, C. "Mathematical Models of Isolation and Quarantine." JAMA: The Journal of the American Medical Association 290, no. 21 (December 3, 2003): 2876–77. http://dx.doi.org/10.1001/jama.290.21.2876.

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22

Eckstein, Shulamith G., and Michal Shemesh. "Mathematical models of cognitive development." British Journal of Mathematical and Statistical Psychology 45, no. 1 (May 1992): 1–18. http://dx.doi.org/10.1111/j.2044-8317.1992.tb00974.x.

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23

Waniewski, Jacek. "Mathematical Models for Peritoneal Transport Characteristics." Peritoneal Dialysis International: Journal of the International Society for Peritoneal Dialysis 19, no. 2_suppl (February 1999): 193–201. http://dx.doi.org/10.1177/089686089901902s32.

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Four mathematical models and for the description of peritoneal transport of fluid solutes are reviewed. The membrane model is usually applied for (1) separation of transport components, (2) formulation of the relationship between flow components and their driving forces, and (3) estimation of transport parameters. The three-pore model provides correct relationships between various transport parameters and demonstrates that the peritoneal membrane should be considered heteroporous. The extended threepore model discriminates between heteroporous capillary wall and tissue layer, which are assumed to be arranged in series; the model improves and modifies the results of the three-pore model. The distributed model includes all parameters involved in peritoneal transport and takes into account the real structure of the tissue with capillaries distributed at various distances from the surface of the tissue. How the distributed model may be applied for the evaluation of the possible impact of perfusion rate on peritoneal transport, as recently discussed for clinical and experimental studies, is demonstrated. The distributed model should provide theoretical bases for the application of other models as approximate and simplified descriptions of peritoneal transport. However, an unsolved problem is the theoretical description of bi-directional fluid transport, which includes ultrafiltration to the peritoneal cavity owing to the osmotic pressure of dialysis fluid and absorption out of the peritoneal cavity owing to hydrostatic pressure.

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24

Flood, R. L., and E. R. Carson. "The Future Role of Mathematical Models in Medicine: A Case Study." IFAC Proceedings Volumes 21, no. 1 (April 1988): 99–102. http://dx.doi.org/10.1016/s1474-6670(17)57540-0.

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25

Bakshi, Suruchi, Vijayalakshmi Chelliah, Chao Chen, and Piet H. van der Graaf. "Mathematical Biology Models of Parkinson's Disease." CPT: Pharmacometrics & Systems Pharmacology 8, no. 2 (November 2, 2018): 77–86. http://dx.doi.org/10.1002/psp4.12362.

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26

Belsole, Robert J., Don R. Hilbelink, J. Anthony Llewellyn, Stephen Stenzler, Thomas L. Greene, and Mark Dale. "Mathematical analysis of computed carpal models." Journal of Orthopaedic Research 6, no. 1 (January 1988): 116–22. http://dx.doi.org/10.1002/jor.1100060115.

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27

Ioannidis, John P. A. "Pre-registration of mathematical models." Mathematical Biosciences 345 (March 2022): 108782. http://dx.doi.org/10.1016/j.mbs.2022.108782.

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28

Fry, D. L. "Mathematical models of arterial transmural transport." American Journal of Physiology-Heart and Circulatory Physiology 248, no. 2 (February 1, 1985): H240—H263. http://dx.doi.org/10.1152/ajpheart.1985.248.2.h240.

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A finite-element model (FEM) and corresponding five-parameter analytical model (AM) were derived to study the one-dimensional transport of chemically reactive macro-molecules across (x) arterial tissue. Derivations emphasize chemical activity [a(x)], its gradient, and water flux as driving forces for chemical reactions and transport. The AM was fitted to 28 measured 125I-albumin transmural concentration [c(x)] curves giving parameter estimates of diffusivity (DA), convective velocity (nu A), and so on as functions of pressure (P), location (z) along the vessel, etc. The FEM was used to study 1) intimal-medial a(x) associated with molecular sieving and medial edema, 2) reversible binding, and 3) errors of AM in analysis of c(x). Results are as follows. Average relative error for the 28 AM fits was 5.3%. Only estimates of DA and nu A had acceptable coefficients of variation. DA (approximately 0.10 X 10(-7) cm2 X s-1) decreased with P, increased with z to a maximum, and then decreased; nu A was approximately proportional to P (approximately 0.12 X 10(-7) cm X s-1 X mmHg-1) and decreased slightly with z; distribution coefficient (epsilon F) decreased with z and was smaller for serum than for simple albumin reagent. Assumed boundary conditions for AM were associated with approximately 1.4% error in AM c(x). Parameter estimates were sensitive to wall inhomogeneity, e.g., approximately 15% error. In conclusion, the AM and FEM simulated measured c(x) well; the FEM is useful for study of mechanisms, experimental designs, and AM errors; trends of AM parameter estimates suggest dependence on P, z, and composition of reagent for further FEM and experimental study.

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29

Souhami, R. L., W. M. Gregory, and B. G. Birkhead. "Mathematical models in high dose chemotherapy." Lung Cancer 5, no. 1 (May 1989): 18–20. http://dx.doi.org/10.1016/0169-5002(89)90191-8.

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30

Melkonian, Vardges. "Mathematical Models for a Social Partitioning Problem." American Journal of Computational Mathematics 11, no. 01 (2021): 1–22. http://dx.doi.org/10.4236/ajcm.2021.111001.

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31

McFarland, Bentson H. "Mathematical models in mental health services research." New Directions for Mental Health Services 1989, no. 44 (1989): 65–72. http://dx.doi.org/10.1002/yd.23319894408.

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32

Kuang, Yang, Meng Fan, Shengqiang Liu, and Wanbiao Ma. "Preface for the Special Issue on Dynamical Models of Biology and Medicine." Applied Sciences 9, no. 11 (June 11, 2019): 2380. http://dx.doi.org/10.3390/app9112380.

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33

Hunt, C. Anthony, Glen E. P. Ropella, Sunwoo Park, and Jesse Engelberg. "Dichotomies between computational and mathematical models." Nature Biotechnology 26, no. 7 (July 2008): 737–38. http://dx.doi.org/10.1038/nbt0708-737.

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34

Fernández-Calvín, Begoña, Juan Orellana, and Domenico Pignone. "Genome Analysis of Triploids Using Mathematical Models." Hereditas 122, no. 1 (May 28, 2004): 41–45. http://dx.doi.org/10.1111/j.1601-5223.1995.00041.x.

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35

Baden, Andrea L. "Social evolution: Mathematical models, mentors, and monkeys." Evolutionary Anthropology: Issues, News, and Reviews 16, no. 4 (August 28, 2007): 159–60. http://dx.doi.org/10.1002/evan.20146.

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36

Carson, Ewart R. "The Role of Dynamic Mathematical Models." Alternatives to Laboratory Animals 13, no. 4 (June 1985): 295–98. http://dx.doi.org/10.1177/026119298501300407.

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37

Kuznetsov, V. A., L. I. Gapon, L. M. Malishevskii, D. S. Lobuntsov, E. A. Dziabenko, A. M. Soldatova, G. S. Pushkarev, V. V. Todosiychuk, and E. I. Yaroslavskaya. "Mathematical models in cardiology: From formulas to real clinical practice." Siberian Journal of Clinical and Experimental Medicine 35, no. 4 (December 25, 2020): 39–48. http://dx.doi.org/10.29001/2073-8552-2020-35-4-39-48.

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Aim. To develop and implement into clinical practice six calculators of risk for various cardiovascular diseases in the form of mobile application for iOS/Android and module for the 1C: Medicine software.Material and Methods. At the premises of Tyumen Cardiology Research Center (TCRC) of Tomsk NRMC, we developed the mobile application for iOS/Android and module for the 1C: Medicine software based on six mathematical models that were invented and patented in our center earlier.Results and Discussion. The use of mobile application improved the convenience of working with the mathematical formulas and reduces the time for obtaining results of calculations. Implementation of 1C as a programming environment allowed to perform automatic filling out the calculator fields with medical data from individual patients, which significantly simplified and accelerated the rate of work with mathematical models.Conclusion. The developed mobile application and external processing for 1C allowed to implement research products of TCRC in the form of mathematical formulas into real-life clinical practice. These developments contributed to speeding up the process for acquisition of results and partial automatization of filling out the form fields.

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38

Curcio, Luciano, Laura D'Orsi, and Andrea De Gaetano. "Seven Mathematical Models of Hemorrhagic Shock." Computational and Mathematical Methods in Medicine 2021 (June 3, 2021): 1–34. http://dx.doi.org/10.1155/2021/6640638.

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Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject’s responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.

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39

Fowler, A. C. "Mathematical Models in the Applied Sciences." Biometrics 54, no. 4 (December 1998): 1684. http://dx.doi.org/10.2307/2533707.

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40

Vodovotz, Yoram, Gilles Clermont, Carson Chow, and Gary An. "Mathematical models of the acute inflammatory response." Current Opinion in Critical Care 10, no. 5 (October 2004): 383–90. http://dx.doi.org/10.1097/01.ccx.0000139360.30327.69.

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41

Iglesias-Puzas, Á., and P. Boixeda. "Deep Learning and Mathematical Models in Dermatology." Actas Dermo-Sifiliográficas (English Edition) 111, no. 3 (April 2020): 192–95. http://dx.doi.org/10.1016/j.adengl.2020.03.005.

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42

Lunyk, T., and I. Cherevko. "DELAY MODELING OF MATHEMATICAL MODELS OF BIOLOGY AND IMMUNOLOGY." Bukovinian Mathematical Journal 9, no. 2 (2021): 92–98. http://dx.doi.org/10.31861/bmj2021.02.07.

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Systems of diﬀerential-diﬀerence equations are mathematical models of many applied problems of biology, ecology, medicine, economics. The variety of mathematical models of real dynamic processes is due to the fact that their evolution does not occur instantaneously, but with some delays that have diﬀerent biological interpretations. The introduction of delay allows you to build adequate mathematical models and describe new eﬀects and phenomena in physics, ecology, immunology and other sciences. The exact solution of diﬀerential-diﬀerence equations can be found only in the simplest cases, so algorithms for ﬁnding approximate solutions of such equations are important. In this paper, a family of diﬀerence schemes is constructed for the approximate ﬁnding of solutions to initial problems with delay. Special cases are generalized Euler diﬀerence schemes. The conditions for the convergence of the generalized explicit Euler diﬀerence scheme are established. To automate the numerical simulation of systems with delays, an application program has been developed, which is used to approximate the solutions of SIR models with two delays.

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43

Rogozinsky, G., M. Chesnokov, and A. Kutlyiarova. "Some New Mathematical Models of Synthesized Sound Signals." Proceedings of Telecommunication Universities 8, no. 2 (June 30, 2022): 76–81. http://dx.doi.org/10.31854/1813-324x-2022-8-2-76-81.

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Modern sound synthesis systems make it possible to implement various signal generation algorithms of higher complexity. The theory of sound synthesis actively uses the mathematical apparatus of analog and digital radio engineering and signal processing, however, it should be noted that the classical signal models used in acoustics are not adequate to real-world synthesized signals, mainly due to the significant complexity of the latter. This article presents some models of synthesized signals typical for practical use.

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44

Trad, Antoine. "Applied Holistic Mathematical Models for Dynamic Systems (AHMM4DS)." International Journal of Cyber-Physical Systems 3, no. 1 (January 1, 2021): 1–24. http://dx.doi.org/10.4018/ijcps.2021010101.

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In this article, the author presents the applied holistic mathematical model for the support of dynamic system (AHMM4DS) transformation and integration processes. The AHMM4DS is based on a mixed research method that is supported by a mainly a qualitative research approach, where the main goal is to insure a strategic business competitive advantage. The AHMM4DS uses a natural programming language (NLP) and factors to support a central reasoning engine and a distributed enterprise architecture project's (EAP) concept. This article's proof of concept (PoC) presents the transformation of a dynamic systems, where the central point is the transformation of their services. A DS is managed by a transformation manager, who uses a methodology and a framework that can support and estimate the risks of implementation of a transformation process. Then he uses it to solve various types of problems. The manager is also responsible for the implementation of the DS, and during its implementation phase a transformation framework is needed.

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45

Gusev, Andrey Olegovich. "Comparison of three mathematical models of directional crystallization." Keldysh Institute Preprints, no. 53 (2022): 1–32. http://dx.doi.org/10.20948/prepr-2022-53.

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The paper provides the comparison of three mathematical models of directional crystallization. The one-dimensional models of crystal growth assuming complete mixing in the melt and no mixing in the melt are examined. The mathematical model of crystallization process in cylindrical ampoule, which accounts for crystallization interface movement, convective heat and mass transfer in the solution, diffusion heat and mass transfer in the crystal, is considered. The ranges of growth regime parameters, for which the simplified models are valid, are determined numerically.

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46

Ojimadu, U. H., A. O. Oluwole, A. O. Olasupo, M. A. Usman, T. J. Odule, O. O. Olubanwo, O. Oyewole, and M. A. Ayodele. "MATHEMATICAL ANALYSIS OF ELECTROPHYSIOLOGICAL CARDIAC TISSUE MEMBRANE MODELS." FUDMA JOURNAL OF SCIENCES 6, no. 2 (May 11, 2022): 138–43. http://dx.doi.org/10.33003/fjs-2022-0602-931.

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This paper presents some cardiac electrophysiological models. Proper mathematical analysis was done on the proposed models. In the cause of the analysis, several assumptions were made which helped in providing a parallel platform for making qualitative solutions so as to reduce any form of bias. Graphical analysis was adopted in solving the cardiac electrophysiological models using conservation and dispersions equations. The results obtained were derived from computer simulation by observing ring lengths on a valid restitution curve. The restitution curves helps us to subject three different turns of ring lengths and certain observations were made on the behavior of the three ring lengths. An increase in ring length will cause a corresponding increase in blood circulation and vice versa. It was suggested that 2D or 3D computer simulation should be adopted for better performance and yield of the models

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47

Budzko, Vladimir, Felix Ereshko, and Michail Gorelov. "Mathematical models of control in Digital Economy platforms." Procedia Computer Science 190 (2021): 115–21. http://dx.doi.org/10.1016/j.procs.2021.06.014.

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48

SACKSTEDER, R. "Comment on Lefebvre's mathematical models by Richard Sacksteder." Journal of Social and Biological Systems 10, no. 2 (April 1987): 227–29. http://dx.doi.org/10.1016/0140-1750(87)90012-1.

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49

Jewell, Nicholas P., Joseph A. Lewnard, and Britta L. Jewell. "Predictive Mathematical Models of the COVID-19 Pandemic." JAMA 323, no. 19 (May 19, 2020): 1893. http://dx.doi.org/10.1001/jama.2020.6585.

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50

Blyumin, S. L., A. V. Galkin, and A. S. Sysoev. "ON SENSITIVITY ANALYSIS BY FACTORS OF MATHEMATICAL MODELS." Mathematical Methods in Technologies and Technics, no. 10 (2022): 39–43. http://dx.doi.org/10.52348/2712-8873_mmtt_2022_10_39.

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Journal articles on the topic 'Medicine – Mathematical models'

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