Mathematical Modelling: Transforming Concepts Into Reality
DOI:
https://doi.org/10.13052/jgeu0975-1416.1312Keywords:
Mathematical modelling, computational techniques, social isolation tacticsAbstract
Mathematical modelling is a powerful tool that bridges the gap between theoretical concepts and real-world phenomena. It involves the development of mathematical equations, algorithms, and computational techniques to describe, analyse, and predict complex systems across various disciplines. Researchers are creating mathematical models based on actual events to meet the demands of this scientific era. The main aim of mathematical modelling is to gain understanding into complex systems, make predictions, and optimize processes. By using mathematical equations, scientists and researchers can simulate and analyse various scenarios, explore the effects of different parameters, and make informed decisions. Mathematical models can provide a better understanding of the given mechanisms governing the system and help uncover relationships and patterns that may not be immediately apparent. Policymakers use mathematical models to inform their choices when deciding on public health interventions like lockdowns, social isolation tactics, and vaccination rollout plans.
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References
Blomhøj, M. (2004). Mathematical modelling: A theory for practice. In International perspectives on learning and teaching mathematics (pp. 145–159). National Center for Mathematics Education.
Blomhøj, M., and Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work: Experiences from an in-service course for upper secondary teachers. ZDM, 38(2), 163–177.
Berry, J., and Houston, K. (1995). Mathematical modelling. Gulf Professional Publishing.
Lahrouz, A., Omari, L., Kiouach, D., and Belmaâti, A. (2011). Deterministic and stochastic stability of a mathematical model of smoking. Statistics & Probability Letters, 81(8), 1276–1284.
Kumar, A., Goel, K., and Nilam. (2020). A deterministic time-delayed SIR epidemic model: mathematical modelling and analysis. Theory in biosciences, 139(1), 67–76.
Steinhoff, J., and Underhill, D. (1994). Modification of the Euler equations for “vorticity confinement”: Application to the computation of interacting vortex rings. Physics of Fluids, 6(8), 2738–2744.
Aguirregabiria, V., and Magesan, A. (2013). Euler equations for the estimation of dynamic discrete choice structural models. In Structural Econometric Models (Vol. 31, pp. 3–44). Emerald Group Publishing Limited.
Mesbah, A. (2016). Stochastic model predictive control: An overview and perspectives for future research. IEEE Control Systems Magazine, 36(6), 30–44.
Valor, A., Caleyo, F., Alfonso, L., Velázquez, J. C., and Hallen, J. M. (2013). Markov chain models for the stochastic modelling of pitting corrosion. Mathematical Problems in Engineering, 2013(1), 108386.
Berthiaux, H., and Mizonov, V. (2004). Applications of Markov chains in particulate process engineering: a review. The Canadian journal of chemical engineering, 82(6), 1143–1168.
Mallet, J. L. (1997). Discrete modelling for natural objects. Mathematical geology, 29, 199–219.
Szabó, B., and Babuška, I. (2021). Finite element analysis: Method, verification and validation.
Krumsiek, J., Pölsterl, S., Wittmann, D. M., and Theis, F. J. (2010). Odefy-from discrete to continuous models. BMC bioinformatics, 11, 1–10.
Ansorge, R., and Sonar, T. (2009). Mathematical models of fluid dynamics: modelling, theory, basic numerical facts-An introduction. John Wiley & Sons.
Norton, T., Sun, D. W., Grant, J., Fallon, R., and Dodd, V. (2007). Applications of computational fluid dynamics (CFD) in the modelling and design of ventilation systems in the agricultural industry: A review. Bioresource technology, 98(12), 2386–2414.
Macal, C. M., and North, M. J. (2009, December). Agent-based modelling and simulation. In Proceedings of the 2009 winter simulation conference (WSC) (pp. 86–98). IEEE.
Scott, G., and Richardson, P. (1997). The application of computational fluid dynamics in the food industry. Trends in Food Science & Technology, 8(4), 119–124.
Caunhye, A. M., Nie, X., and Pokharel, S. (2012). Optimization models in emergency logistics: A literature review. Socio-economic planning sciences, 46(1), 4–13.
Sawik, B. (2023). Space mission risk, sustainability and supply chain: review, multi-objective optimization model and practical approach. Sustainability, 15(14), 11002.
McCullagh, P. (2002). What is a statistical model?. The Annals of Statistics, 30(5), 1225–1310.
van de Schoot, R., Depaoli, S., King, R., Kramer, B., Märtens, K., Tadesse, M. G., … and Yau, C. (2021). Bayesian statistics and modelling. Nature Reviews Methods Primers, 1(1), 1.
English, L. D., and Halford, G. S. (2012). Mathematics education: Models and processes. Routledge.
Lindell, D. B., Martel, J. N., and Wetzstein, G. (2021). Autoint: Automatic integration for fast neural volume rendering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 14556–14565).
Fornberg, B. (2021). Improving the accuracy of the trapezoidal rule. SIAM Review, 63(1), 167–180.
Venkateshan, S. P., and Swaminathan, P. (2023). Numerical integration. In Computational Methods in Engineering (pp. 353–440). Cham: Springer International Publishing.
Kaiser, G. (2020). Mathematical modelling and applications in education. Encyclopedia of mathematics education, 553–561.
Mayovets, Y., Vdovenko, N., Shevchuk, H., Zos-Kior, M., and Hnatenko, I. (2021). Simulation modelling of the financial risk of bankruptcy of agricultural enterprises in the context of COVID-19. Journal of Hygienic Engineering and Design. 2021. Vol. 36. P. 192–198.
Kaczor, Z., Buliński, Z., and Werle, S. (2020). modelling approaches to waste biomass pyrolysis: a review. Renewable Energy, 159, 427–443.
