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Journal articles on the topic 'Freshwater microbiology mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Chiyaka, Edward T., Gesham Magombedze, and Lawrence Mutimbu. "Modelling within Host Parasite Dynamics of Schistosomiasis." Computational and Mathematical Methods in Medicine 11, no. 3 (2010): 255–80. http://dx.doi.org/10.1080/17486701003614336.

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Schistosomiasis infection is characterized by the presence of adult worms in the portal and mesenteric veins of humans as part of a complex migratory cycle initiated by cutaneous penetration of the cercariae shed by infected freshwater snails. The drug praziquantel is not always effective in the treatment against schistosomiasis at larvae stage. However, our simulations show that it is effective against mature worms and eggs. As a result, the study and understanding of immunological responses is key in understanding parasite dynamics. We therefore introduce quantitative interpretations of human immunological responses of the disease to formulate mathematical models for the within-host dynamics of schistosomiasis. We also use numerical simulations to demonstrate that it is the level of T cells that differentiates between either an effective immune response or some degree of infection. These cells are responsible for the differentiation and recruitment of eosinophils that are instrumental in clearing the parasite. From the model analysis, we conclude that control of infection is much attributed to the value of a functionf, a measure of the average number of larvae penetrating a susceptible individual having hatched from an egg released by an infected individual. This agrees with evidence that there is a close association between the ecology, the distribution of infection and the disease.

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2

Stelling, Jörg. "Mathematical models in microbial systems biology." Current Opinion in Microbiology 7, no. 5 (October 2004): 513–18. http://dx.doi.org/10.1016/j.mib.2004.08.004.

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3

Costanza, Robert, and Fred H. Sklar. "Articulation, accuracy and effectiveness of mathematical models: A review of freshwater wetland applications." Ecological Modelling 27, no. 1-2 (March 1985): 45–68. http://dx.doi.org/10.1016/0304-3800(85)90024-9.

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4

Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.2307/30141966.

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5

Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.1086/647503.

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6

Li, Hao, Guozhong Xie, and Alan S. Edmondson. "Review of Secondary Mathematical Models of Predictive Microbiology." Journal of Food Products Marketing 14, no. 2 (May 28, 2008): 57–74. http://dx.doi.org/10.1080/10454440801918283.

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7

Grassly, Nicholas C., and Christophe Fraser. "Mathematical models of infectious disease transmission." Nature Reviews Microbiology 6, no. 6 (May 13, 2008): 477–87. http://dx.doi.org/10.1038/nrmicro1845.

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8

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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9

Bao, Weijun, Songming Zhu, Shuirong Guo, Li Wang, Shixue Huang, Jingyi Fu, and Zhangying Ye. "Particle size distribution mathematical models and properties of suspended solids in a typical freshwater pond." Environmental Pollution 241 (October 2018): 164–71. http://dx.doi.org/10.1016/j.envpol.2018.05.063.

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10

Shang, Qian Ming. "Modeling and Simulation of Freshwater Generator Subsystem of Low Speed Engine Room Simulator Based on Visual." Advanced Materials Research 557-559 (July 2012): 2324–28. http://dx.doi.org/10.4028/www.scientific.net/amr.557-559.2324.

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3d models of the equipments of freshwater generator system are built according to the real ship. In support of a simulative sustainable system, a real-time variable database and mathematical models of the subsystem are set up. Then the precision of the models are proved to meet the demands by comparing the simulation results with the practical situation. The interfaces are available by making use of VC++6.0. Finally, the data connections between the math models and interfaces are established by means of the technology of network communications. The purpose of developing this simulation system is training, which offers students a chance to make a good knowledge of the structure and working principle of the freshwater generator subsystem.

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11

Li, Hao, Guozhong Xie, and Alan Edmondson. "Evolution and limitations of primary mathematical models in predictive microbiology." British Food Journal 109, no. 8 (August 14, 2007): 608–26. http://dx.doi.org/10.1108/00070700710772408.

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12

Black, F. L., and B. Singer. "Elaboration Versus Simplification in Refining Mathematical Models of Infectious Disease." Annual Review of Microbiology 41, no. 1 (October 1987): 677–701. http://dx.doi.org/10.1146/annurev.mi.41.100187.003333.

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13

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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14

Assab, Rania, Narimane Nekkab, Pascal Crépey, Pascal Astagneau, Didier Guillemot, Lulla Opatowski, and Laura Temime. "Mathematical models of infection transmission in healthcare settings." Current Opinion in Infectious Diseases 30, no. 4 (August 2017): 410–18. http://dx.doi.org/10.1097/qco.0000000000000390.

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15

López, S., M. Prieto, J. Dijkstra, M. S. Dhanoa, and J. France. "Statistical evaluation of mathematical models for microbial growth." International Journal of Food Microbiology 96, no. 3 (November 2004): 289–300. http://dx.doi.org/10.1016/j.ijfoodmicro.2004.03.026.

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16

Nokes, D. J., and R. M. Anderson. "Application of mathematical models to the design of immunization strategies." Reviews in Medical Microbiology 4, no. 1 (January 1993): 1–7. http://dx.doi.org/10.1097/00013542-199301000-00001.

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17

Lopatin, A. A., E. V. Kuklev, V. A. Safronov, A. S. Razdorsky, L. V. Samoilova, and V. P. Toporkov. "Verification of Mathematical Models of Plague." Problems of Particularly Dangerous Infections, no. 3(113) (June 20, 2012): 26–28. http://dx.doi.org/10.21055/0370-1069-2012-3-26-28.

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Mathematic modeling and prognostication of infectious diseases epidemic process is a promising trend of epidemiologic investigations. The complex of mathematic models (SEIRF type) of plague epidemic process was developed for this purpose by the Russian Research Anti-Plague Institute “Microbe” and laboratory of epidemiologic cybernetics of N.F.Gamaleya Institute for Epidemiology and Microbiology. The data on the plague outbreak in 1945 in the rural settlement Avan’ (Aral region of Kzyl-Orda district of Kazakh SSR) were used to test working efficiency of this complex. The data analysis permitted to obtain the starting and boundary conditions for epidemic process modeling. In the process of modeling the mathematical models of epidemic process of plague with various ways of infection transmission for each epidemic focus in regard with historical data were used. The data were processed by the analytical platform Deductor 5.1. Identified was strong positive correlation between estimated and historical data – r = +0,71. The results received testify that mathematic models are effective and give high degree of confidence. They can be used to receive quantitative characteristics of prognosis for plague epidemic process development with different transmission routes considering that anti-epidemic measures have been taken.

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18

Navarro, Antonio R. "Effects of furfural on ethanol fermentation bySaccharomyces cerevisiae: Mathematical models." Current Microbiology 29, no. 2 (August 1994): 87–90. http://dx.doi.org/10.1007/bf01575753.

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19

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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20

WALLS, ISABEL, VIRGINIA N. SCOTT, and DANE T. BERNARD. "Validation of Predictive Mathematical Models Describing Growth of Staphylococcus aureus." Journal of Food Protection 59, no. 1 (January 1, 1996): 11–15. http://dx.doi.org/10.4315/0362-028x-59.1.11.

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An investigation was performed on the growth of Staphylococcus aureus in a commercially available, sterile, homogeneous food at 12°C with 1.2 and 5.9% NaCl; at 25°C with 10.4% NaCl; and at 20 and 35°C with 1.2, 5.3, 12.5, and 15.8% NaCl; over a pH range of 5.5 to 7.5. Growth data were fitted to the Gompertz equation and the resulting growth kinetics were compared with predictions from the Pathogen Modeling Program (PMP) and Food MicroModel (FMM). For the PMP, predicted lag-phase durations varied from 0.5 to 130 h longer than the observed values. In general, close agreement with growth rates was obtained but there was a 10-fold difference in one case. For FMM, predicted lag-phase durations ranged from 27 h shorter to 47 h longer than the observed values. Again, close agreement with growth rates was obtained, but in one case a fivefold difference was observed. In general, for the sterile foods used under the growth conditions tested, the models underestimated the growth of S. aureus. This implies that while the models can be used as a guide to indicate growth rates in foods they should not be relied upon as the sole determinant of the product's safety.

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21

Mayank, Rahul, Amrita Ranjan, and Vijayanand S. Moholkar. "Mathematical models of ABE fermentation: review and analysis." Critical Reviews in Biotechnology 33, no. 4 (October 16, 2012): 419–47. http://dx.doi.org/10.3109/07388551.2012.726208.

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22

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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23

Drancourt, M., and D. Raoult. "Value of mathematical models for epidemics: the plague paradigm." Clinical Microbiology and Infection 25, no. 1 (January 2019): 120. http://dx.doi.org/10.1016/j.cmi.2018.08.014.

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24

WALLS, ISABEL, and VIRGINIA N. SCOTT. "Validation of Predictive Mathematical Models Describing the Growth of Listeria monocytogenes." Journal of Food Protection 60, no. 9 (September 1, 1997): 1142–45. http://dx.doi.org/10.4315/0362-028x-60.9.1142.

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Growth of Listeria monocytogenes and Listeria innocua in commercially available sterile homogeneous foods was investigated at different temperatures, pH values, and NaCl concentrations. Growth data were fitted to the Gompertz equation and the resulting growth kinetics were compared with predictions from the Pathogen Modeling Program and Food MicroModel. In general, good agreement was obtained when comparing growth rates and generation times for both models. Differences were observed when comparing lag phases, which ranged from 117 h shorter to 4.9 h longer than predicted for L. monocytogenes. Despite differences in lag phase, under most conditions, the models gave good predictions of microbial growth. Predictive modeling appears to be a useful tool in determining growth rates of Listeria in foods.

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25

Bouzouf, Boutaina, and Zhi Chen. "A comparison of finite volume method and sharp model for two dimensional saltwater intrusion modeling." Canadian Journal of Civil Engineering 41, no. 3 (March 2014): 191–96. http://dx.doi.org/10.1139/cjce-2013-0265.

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Seawater intrusion in coastal aquifers is a 3-D phenomenon. However, 3-D regional aquifer models are often limited by insufficient geological and hydrological data, the large horizontal to vertical scales ratio, and by numerical constraints. A mathematical formulation and numerical implementation of the model for saltwater intrusion problems are presented in this paper. The mathematical model is based on assumption of two-phase flow between saltwater and freshwater and Dupuit approximation. Finite volume method is used as the numerical method in non-structured grids to have flexibility upon complex configuration domain and was compared to sharp model that uses finite difference method. Both models are based on the same governing mathematical equations. Finite volume method was validated using analytical test case studies with known closed form solutions, and the results showed good agreement. Both models have then been applied to the case of saltwater intrusion into a real study case. The comparison between both methods indicates that the finite volume method provides predictions closer to the observed results.

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26

Policastro, Grazia, Vincenzo Luongo, Luigi Frunzo, and Massimiliano Fabbricino. "A comprehensive review of mathematical models of photo fermentation." Critical Reviews in Biotechnology 41, no. 4 (February 18, 2021): 628–48. http://dx.doi.org/10.1080/07388551.2021.1873241.

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27

Michelson, Seth. "Multidrug restistance and its reversal: mathematical models." Computational and Mathematical Methods in Medicine 2, no. 1 (1999): 103–15. http://dx.doi.org/10.1080/10273669908833032.

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28

Moser, A., B. Mayr, W. Jury, W. Steiner, and P. Horvat. "Mathematical models for mixing in deep jet bioreactors: analysis." Bioprocess Engineering 7, no. 4 (December 1991): 171–76. http://dx.doi.org/10.1007/bf00387413.

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29

Puskas, James, Edward McBean, and Nicholas Kouwen. "Behaviour and transport of oil under smooth ice." Canadian Journal of Civil Engineering 14, no. 4 (August 1, 1987): 510–18. http://dx.doi.org/10.1139/l87-075.

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Mathematical and physical models are used in studying transport of oil slicks beneath ice in the presence of an ambient water current. The mathematical expressions for the relevant forces are developed by utililizing basic boundary layer theory and considering the physical properties of the oils and are verified from the laboratory experiments. Three different crude oils are utilized beneath freshwater ice under various flow conditions in the experiments.The transport of oil slicks oriented longitudinally to the direction of the water flow are modelled by the summation of the shear force at the oil – water interface and the oil – ice friction force. Oil slicks oriented transverse to the direction of the water flow are subjected to an additional form-drag force acting as the primary driving force.For oils with low viscosities, the oil – ice friction force can be approximated by assuming "no-slip" at the oil – ice interface. Oils with high viscosities move almost as a solid mass, with the majority of the velocity variation taking place in a thin water film separating the oil and the ice. Key words: boundary layer theory, environmental engineering, ice, mathematical models, oil spills, physical models.

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30

Britton, N. F. "Review: Mathematical Models in Biology: An Introduction." Mathematical Medicine and Biology: A Journal of the IMA 22, no. 3 (September 1, 2005): 289–90. http://dx.doi.org/10.1093/imammb/dqi008.

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31

Zhou, Zhifang, Boran Zhang, Qiaona Guo, and Shumei Zhu. "Experimental and Numerical Studies on the Vertical Flow of Variable Density Fluid in Different Directions." Geofluids 2019 (April 24, 2019): 1–15. http://dx.doi.org/10.1155/2019/2175983.

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Injecting freshwater and pumping salt water are effective methods to restore the salt water in a coastal area. Based on a one-dimensional vertical experiment, the variable density flow is simulated under the condition of different injection directions and injection rates of fresh water. A one-dimensional mathematical model of variable density flow and solute transport is established. The mathematical models are solved using the implicit difference method. Fortran code is developed to simulate and verify the vertical flow of variable density flow in different directions. Through both numerical simulation and experimental studies, it is found that the variable density fluid in the direction of reverse gravity is different from that in the direction of gravity. On this basis, the most effective desalination model of salt water is further discussed. It provides a theoretical and technical method for the restoration of salt water in the vertical injection of freshwater. In order to improve the remediation efficiency and reduce the cost in the engineering application, the suitable water injection rate should be ensured, considering the suitable construction time and zone of a study area.

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32

Vilyunov, Sergey D. "Study of the contribution of horizontal stability in the probability model of the “hostpathogen” interaction system on the basis of millet varieties susceptible to smut." Agrarian science, no. 11-12 (January 20, 2021): 97–100. http://dx.doi.org/10.32634/0869-8155-2020-343-11-97-100.

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Digital control of breeding process, creation of mathematical models of living objects and management of plant life cycle is an urgent problem of modern times. Сreation of technologies that ensure implementation of the concept of advanced digital "smart" agriculture is impossible without basic mathematical models of "mass interactions" of natural living objects. This primarily affects the spread of certain diseases in populations. In the plant world, such a convenient model object is the well-studied "host-pathogen" system by the example of the interaction of millet and its smut disease. At present, the knowledge of the patterns of development of this disease in the millet plant is of a qualitative nature (virulence), and the quantitative characteristics (aggressiveness) are approximate. Only mathematical modeling of this process can accurately describe the development of the disease. This paper examines a probabilistic model and certain aspects of mathematical modeling using the example of identifying the laws of horizontal resistance to smut in susceptible millet genotypes.

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33

Curto, Raul, Eberhard O. Voit, Albert Sorribas, and Marta Cascante. "Mathematical models of purine metabolism in man." Mathematical Biosciences 151, no. 1 (July 1998): 1–49. http://dx.doi.org/10.1016/s0025-5564(98)10001-9.

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34

Amuzescu, Bogdan, Razvan Airini, Florin Bogdan Epureanu, Stefan A. Mann, Thomas Knott, and Beatrice Mihaela Radu. "Evolution of mathematical models of cardiomyocyte electrophysiology." Mathematical Biosciences 334 (April 2021): 108567. http://dx.doi.org/10.1016/j.mbs.2021.108567.

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35

Gutarowska, B., and Z. Żakowska. "Mathematical models of mycelium growth and ergosterol synthesis in stationary mould culture." Letters in Applied Microbiology 48, no. 5 (May 2009): 605–10. http://dx.doi.org/10.1111/j.1472-765x.2009.02577.x.

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36

Weeks, Stephen C., Thomas F. Sanderson, Sadie K. Reed, Magdalena Zofkova, Brenton Knott, Usha Balaraman, Guido Pereira, Diana M. Senyo, and Walter R. Hoeh. "Ancient androdioecy in the freshwater crustacean Eulimnadia." Proceedings of the Royal Society B: Biological Sciences 273, no. 1587 (December 6, 2005): 725–34. http://dx.doi.org/10.1098/rspb.2005.3370.

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Among the variety of reproductive mechanisms exhibited by living systems, one permutation—androdioecy (mixtures of males and hermaphrodites)—is distinguished by its rarity. Models of mating system evolution predict that androdioecy should be a brief stage between hermaphroditism and dioecy (separate males and females), or vice versa. Herein we report evidence of widespread and ancient androdioecy in crustaceans in the genus Eulimnadia , based on observations of over 33 000 shrimp from 36 locations from every continent except Antarctica. Using phylogenetic, biogeographical and palaeontological evidence, we infer that androdioecy in Eulimnadia has persisted for 24–180 million years and has been maintained through multiple speciation events. These results suggest that androdioecy is a highly successful aspect of the life history of these freshwater crustaceans, and has persisted for orders of magnitude longer than predicted by current models of this rare breeding system.

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37

CASTILLEJO-RODRÍGUEZ, A. M., R. M. GARCÍA GIMENO, G. ZURERA COSANO, E. BARCO ALCALÁ, and M. R. RODRÍGUEZ PÉREZ. "Assessment of Mathematical Models for Predicting Staphylococcus aureus Growth in Cooked Meat Products." Journal of Food Protection 65, no. 4 (April 1, 2002): 659–65. http://dx.doi.org/10.4315/0362-028x-65.4.659.

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The growth of Staphylococcus aureus in commercially available vacuum-packaged cooked ham, turkey breast meat, and chicken breast meat stored at 2.3, 6.5, 10, 13.5, and 17.7°C was studied. Growth rates observed in these food products were compared with those predicted on the basis of various growth models found in the literature and with those generated by the Pathogen Modeling Program and the Food MicroModel software using graphical and mathematical analysis for performance evaluation. In general, the models studied overestimated the growth of S. aureus. The Dengremont and Membré model most closely matched the observed behavior of S. aureus in ham and chicken breast meat, with bias factors of 1.56 and 1.09, respectively. The Eifert et al. model accurately described the growth of S. aureus in turkey breast meat, with a bias factor of 1.51. The remaining models provided safe predictions of the growth rate of S. aureus, but with poor accuracy. Predictive microbiology models have an immediate practical application in improving microbial food safety and quality and are very useful decision support tools, but they should not be used as the sole determinant of product safety.

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38

Zhani, Khalifa, and Khaled Ali Abuhasel. "Modeling, Simulation, and Optimization of a Solar-Based System of Desalination Using Humidification and Dehumidification." Applied Sciences 10, no. 10 (May 13, 2020): 3361. http://dx.doi.org/10.3390/app10103361.

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Solar desalination systems are characterized by low freshwater production compared with the usual techniques of mineral and salt removal from water. The usual methods include, but are not limited to, multi-stage flash distillation, multiple-effect distillation, vapor-compression desalination, and reverse osmosis. Solar desalination requires various modifications to make it more productive than the usual methods. The method is suitable for energy and environmental protection, making it the most effective system. The adjustments involve using the humidification and dehumidification principle (HD). The three configurations of the HD solar desalination system in this project are designed to accommodate variations in climate conditions and seasonal changes. Mathematical models are designed to test the workability of the system in an ideal environment. The models are based on universal fluid equations that regulate the functioning of each component of the system. After the model is designed, a regulation algorithm is designed based on the model. The simulation results show that the gain in freshwater production using a regulation algorithm is in the order of 33%.

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39

Vila, X., C. A. Abella, J. B. Figueras, and J. P. Hurley. "Vertical models of phototrophic bacterial distribution in the metalimnetic microbial communities of several freshwater North-American kettle lakes." FEMS Microbiology Ecology 25, no. 3 (March 1998): 287–99. http://dx.doi.org/10.1111/j.1574-6941.1998.tb00481.x.

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40

Nicolaï, Bart M., Jan F. Van Impe, Peter A. Vanrolleghem, and Joos Vandewalle. "Evaluation of two unstructured mathematical models for the penicillin G fedbatch fermentation." Antonie van Leeuwenhoek 62, no. 4 (November 1992): 273–83. http://dx.doi.org/10.1007/bf00572595.

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41

Pruitt, Kenneth M., and David N. Kamau. "Mathematical models of bacterial growth, inhibition and death under combined stress conditions." Journal of Industrial Microbiology 12, no. 3-5 (September 1993): 221–31. http://dx.doi.org/10.1007/bf01584194.

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42

Yue, Li Hong, and Yi Peng Yang. "Study on Light Intensity Attenuation Characteristics of Chlorella Sp. Culture and the Growth of Chlorella Sp. with the Gradient Light Illuminate Culture." Applied Mechanics and Materials 675-677 (October 2014): 86–89. http://dx.doi.org/10.4028/www.scientific.net/amm.675-677.86.

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Based on the photoautotrophic characteristics of the freshwater microalage, light intensity attenuation characteristics in the cell culture system for Chlorella sp. were studied. Micralgae was cultured with a constant and the gradient light illuminate culture conditions, the cell growth of Microlagae was detected respectively, By means of regression analysis, mathematical models of illuminance intensity attenuation are gotten under different culture conditions. Results show algae cell density under gradient light culture conditions is higher than constant light, so the gradient light is more suitable for the cultivation of microalgae.

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43

Adkison, Milo D. "Models of the effects of marine-derived nutrients on salmon (Oncorhynchus spp.) population dynamics." Canadian Journal of Fisheries and Aquatic Sciences 67, no. 1 (January 2010): 5–15. http://dx.doi.org/10.1139/f09-161.

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Pacific salmon ( Oncorhynchus spp.) populations transfer large quantities of nutrients from their marine to their freshwater habitats. These nutrients have been shown to affect salmon populations in fresh water, including increasing basal food resources and elevating juvenile salmon growth rates and condition. The broader effects on recruitment and commercial harvests, however, are not clear. I developed and explored mathematical models of the effects of these nutrients on stock–recruitment relationships and used these models to investigate management implications. Populations strongly dependent on nutrients had lower sustained yields than those not dependent on nutrients. When nutrients strongly affected the stock–recruitment relationship, relatively low harvest rates and high escapement levels were necessary to maintain the population’s productivity. However, in some scenarios, the highest yields were obtained from small, nutrient-depleted populations. In other scenarios, the nutrient dependence had few management implications.

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44

Layton, Anita T. "His and her mathematical models of physiological systems." Mathematical Biosciences 338 (August 2021): 108642. http://dx.doi.org/10.1016/j.mbs.2021.108642.

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45

Li, Songjun, Pingchu Chen, Wuke Li, Xiao Hao, and Guangfu Yang. "Establishing Mathematical and Physical Models for the Adsorption of Biomacromolecules." Applied Biochemistry and Biotechnology 134, no. 2 (2006): 165–78. http://dx.doi.org/10.1385/abab:134:2:165.

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46

Schwippel, J., and J. Votruba. "Identification of mathematical models of complex cultures of microorganisms in continuous cultivation—Numerical approach." Folia Microbiologica 37, no. 6 (December 1992): 427–32. http://dx.doi.org/10.1007/bf02899901.

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47

SCHAFFNER, DONALD W. "Utilization of Mathematical Models To Manage Risk of Holding Cold Food without Temperature Control." Journal of Food Protection 76, no. 6 (June 1, 2013): 1085–94. http://dx.doi.org/10.4315/0362-028x.jfp-12-424.

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This document describes the development of a tool to manage the risk of the transportation of cold food without temperature control. The tool uses predictions from ComBase predictor and builds on the 2009 U.S. Food and Drug Administration Model Food Code and supporting scientific data in the Food Code annex. I selected Salmonella spp. and Listeria monocytogenes as the organisms for risk management. Salmonella spp. were selected because they are associated with a wide variety of foods and grow rapidly at temperatures >17°C. L. monocytogenes was selected because it is frequently present in the food processing environment, it was used in the original analysis contained in the Food Code Annex, and it grows relatively rapidly at temperatures <17°C. The suitability of a variety of growth models under changing temperature conditions is largely supported by the published literature. The ComBase predictions under static temperature conditions were validated using 148 ComBase database observations for Salmonella spp. and L. monocytogenes in real foods. The times and temperature changes encompassed by ComBase Predictor models for Salmonella spp. and L. monocytogenes are consistent with published data on consumer food transport to the home from the grocery store and on representative foods from a wholesale cash and carry food service supplier collected as part of this project. The resulting model-based tool will be a useful aid to risk managers and customers of wholesale cash and carry food service suppliers, as well as to anyone interested in assessing and managing the risks posed by holding cold foods out of temperature control in supermarkets, delis, restaurants, cafeterias, and homes.

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Moser, A., B. Mayr, W. Jury, W. Steiner, and P. Horvat. "Mathematical models for mixing in deep-jet bioreactors: Calculation of parameters." Bioprocess Engineering 7, no. 4 (December 1991): 177–82. http://dx.doi.org/10.1007/bf00387414.

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Meyerhoff, J., and K. H. Bellgardt. "Two mathematical models for the development of a single microbial pellet." Bioprocess Engineering 12, no. 6 (May 1995): 315–22. http://dx.doi.org/10.1007/bf00369508.

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Maini, Philip K. "Using mathematical models to help understand biological pattern formation." Comptes Rendus Biologies 327, no. 3 (March 2004): 225–34. http://dx.doi.org/10.1016/j.crvi.2003.05.006.

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