nach oben

Mathematical Models and Computer Simulations

Erschienen in:

01.12.2022

Intelligent Local Search for an Optimal Control of Diabetic Population Dynamics

verfasst von: El Ouissari Abdellatif, El Moutaouakil Karim, Baïzri Hicham, Chellak Saliha

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 6/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Diabetes is a chronic disease that affects millions of people in the world. This work has two objectives: (a) elaboration of a state of the art on the different dynamic systems with economic function proposed in the literature controlling diabetes in order to alleviate the socio-economic damage caused by it; (b) implementation of the best performing local search artificial intelligence methods (metaheuristics) to solve the kernel model dealing with the common compartments between all these models. The idea behind the use of metaheuristics is that these intelligent methods are able to provide an excellent approximation of a very economical control marked by its continuity and which does not completely exhaust the human and material resources programmed for the control of the studied phenomenon. Our work is marked by a richness of experiments allowing to analyze several interesting aspects of the phenomenon: quality of the control, cost of the control, and behavior of the different compartments in the presence of the control. In comparison with bees algorithm (BA), firefly algorithm (FA), particle swarm algorithm (PSO), genetic algorithm (GA), moth swarm algorithm (MSA), stochastic fractal search (SFS), wind driven optimization (WDO), and probabilistic bees algorithm (PBA). The stochastic fractal search (SFS) method has shown an unprecedented ability to produce continuous, economical controls capable of alleviating socio-economic damage against a reasonable budget.

Vorheriger Artikel An Alternative Formalism for the Single-Heated Channel Numerical Analysis

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

World Health Organisation, Definition and diagnosis of diabetes mellitus and intermediate hyperglycemia: Report of a WHO/IDF Consultation (WHO, Geneva, 2016).

International Diabetes Federation, IDF Diabetes Atlas, 9th ed. (IDF, Brussels, 2019).

A. Boutayeb, E. H. Twizell, K. Achouayb, and A. Chetouani, “A mathematical model for the burden of diabetes and its complications,” Biomed. Eng. Online 3, 20, 1–8 (2004). https://doi.org/10.1186/1475-925X-3-20CrossRef

A. Boutayeb, A. Chetouani, A. Achouyab, and E. H. Twizell, “A non-linear population model of diabetes mellitus,” J. Appl. Math. Comput. 21 (1), 127–139 (2006). https://doi.org/10.1007/BF02896393MathSciNetCrossRefMATH

A. Kouidere, O. Balatif, H. Ferjouchia, A. Boutayeb, and M. Rachik, “Optimal control strategy for a discrete time to the dynamics of a population of diabetics with highlighting the impact of living environment,” Discrete Dyn. Nat. Soc. 2019, 6342169 (2019). https://doi.org/10.1155/2019/6342169MathSciNetCrossRefMATH

A. Boutayeb, and A. Chetouani, “A population model of diabetes and prediabetes,” Int. J. Comput. Math. 84 (1), 57–66 (2007). https://doi.org/10.1080/00207160601167037MathSciNetCrossRefMATH

A. Kouidere, A. Labzai, H. Ferjouchia, O. Balatif, and M. Rachik, “A new mathematical modeling with optimal control strategy for the dynamics of oopulation of diabetics and its complications with effect of behavioral factors,” J. Appl. Math. 2020, 1943110 (2020). https://doi.org/10.1155/2020/1943410CrossRefMATH

A. Kouidere, B. Khajji, O. Balatif, and M. Rachik, “A multi-age mathematical modeling of the dynamics of population diabetics with effect of lifestyle using optimal control,” J. Appl. Math. Comput. 67 (1–2), 375–403 (2021). https://doi.org/10.1007%2Fs12190-020-01474-w

M. Derouich, A. Boutayeb, W. Boutayeb, and M. Lamlili, “Optimal control approach to the dynamics of a population of diabetics,” Appl. Math. Sci. 8 (56), 2773–2782 (2014). https://doi.org/10.12988/ams.2014.43155CrossRef

10.

A. Mahata, S. P. Mondal, S. Alam, A. Chakraborty, S. K. De, and A. Goswami, “Mathematical model for diabetes in fuzzy environment with stability analysis,” J. Intell. Fuzzy Syst. 36 (3), 2923–2932 (2019). https://doi.org/10.3233/JIFS-171571CrossRef

11.

R. L. Ollerton, “Application of optimal control theory to diabetes mellitus,” Int. J. Control 50 (6), 2503–2522 (1989). https://doi.org/10.1080/00207178908953512MathSciNetCrossRefMATH

12.

G. W. Swan, “An optimal control model of diabetes mellitus,” Bull. Math. Biol. 44 (6), 793–808 (1982). https://doi.org/10.1016/S0092-8240(82)80043-8MathSciNetCrossRefMATH

13.

A. Makroglou, I. Karaoustas, J. Li, and Y. Kuang, “Delay differential equation models in diabetes modeling: A review,” in Encyclopedia of Life Support Systems (EOLSS), Mathematical Physiology, Ed. by A. de Gaetano and P. Palumbo, Developed under the Auspices of the UNESCO (EOLSS Publishers, Oxford, UK, 2011). http://www.eolss.net/Sample-Chapters/C02/E6-188-14.pdf.

14.

A. B. Gumel, P. N. Shivakumar, and B. M. Sahai, “A mathematical model for the dynamics of HIV-1 during the typical course of infection,” in Proc. 3rd World Congress of Nonlinear Analysts, Nonlinear Anal.: Theory, Methods Appl. 47 (3), 1773–1783 (2001). https://doi.org/10.1016/S0362-546X(01)00309-1

15.

D. T. Pham, A. Ghanbarzadeh, E. Koç, S. Otri, S. Rahim, and M. Zaidi, Bee algorithm: A novel approach to function optimization, Technical Note MEC 0501 (Manufacturing Engineering Centre, Cardiff University, UK, 2005).

16.

H. R. Nasrinpour, A. Massah Bavani, and M. Teshnehlab, “Grouped Bees Algorithm: A grouped version of the Bees Algorithm,” Computers 6 (1), 5 (2017). https://doi.org/10.3390/computers6010005CrossRef

17.

D. T. Pham and A. Haj Darwish, “Fuzzy selection of local search sites in the Bees Algorithm,” in Innovative Production Machines and Systems: 4th I*PROMS Virtual International Conference (IPROMS 2008) (Cardiff University, Cardiff, UK, 2008).

18.

Q. T. Pham, D. T. Pham, and M. Castellani, “A modified Bees Algorithm and a statistics-based method for tuning its parameters,” Proc. Inst. Mech. Eng., Part I 226 (3), 287–301 (2012). https://doi.org/10.1177/0959651811422759CrossRef

19.

X.-S. Yang, Nature-Inspired Metaheuristic Algorithms (Luniver Press, Frome, UK, 2008).

20.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. ICNN’95 – International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December, 1995 (IEEE, 1995), Vol. 4, pp. 1942–1948. https://doi.org/10.1109/ICNN.1995.488968.

21.

M. Taherkhani and R. Safabakhsh, “A novel stability-based adaptive inertia weight for particle swarm optimization,” Appl. Soft Comput. 38, 281–295 (2016). https://doi.org/10.1016/j.asoc.2015.10.004CrossRef

22.

A.-A. A. Mohamed, Y. S. Mohamed, A. A. M. El-Gaafary, et al., “Optimal power flow using moth swarm algorithm,” Electr. Power Syst. Res. 142, 190–206 (2017). https://doi.org/10.1016/j.epsr.2016.09.025CrossRef

23.

Z. Bayraktar, M. Komurcu, and D. H. Werner, “Wind Driven Optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics,” in 2010 IEEE Antennas and Propagation Society International Symposium, Toronto, Canada, July 11–17, 2010 (IEEE. 2010), pp. 1–4. https://doi.org/10.1109/APS.2010.5562213

24.

H. Salimi, “Stochastic fractal search: A powerful metaheuristic algorithm,” Knowl.-Based Syst. 75, 1–18 (2015). https://doi.org/10.1016/j.knosys.2014.07.025CrossRef

25.

P. Bogacki and L. F. Shampine, “A 3(2) pair of Runge–Kutta formulas,” Appl. Math. Lett. 2 (4), 321–325 (1989). https://doi.org/10.1016/0893-9659(89)90079-7MathSciNetCrossRefMATH

26.

T. T. Yusuf, “Optimal control of incidence of medical complications in a diabetic patients’ population,” FUTA J. Res. Sci. 11 (1), 180–189 (2015).

27.

A. H. Permatasari, R. H. Tjahjana, and T. Udjiani, “Existence and characterization of optimal control in mathematics model of diabetics population,” J. Phys.: Conf. Ser. 983, 012069 (2018). https://doi.org/10.1088/1742-6596/983/1/012069CrossRef

28.

A. A. M. Daud, C. Q. Toh, and S. Saidun, “Development and analysis of a mathematical model for the population dynamics of Diabetes Mellitus during pregnancy,” Math. Models Comput. Simul. 12 (4), 620–630 (2020). https://doi.org/10.1134/S2070048220040067MathSciNetCrossRef

29.

H. W. Sorenson, “Least-squares estimation: from Gauss to Kalman,” IEEE Spectrum 7 (7), 63–68 (1970). https://doi.org/10.1109/MSPEC.1970.5213471CrossRef

30.

J. L. Crassidis and J. L. Junkins, Optimal Estimation of Dynamic Systems (Chapman & Hall/CRC, Boca Raton, FL, 2004). https://doi.org/10.1201/9780203509128CrossRefMATH

31.

M. Medvedeva, T. E. Simos, C. Tsitouras, and V. Katsikis, “Direct estimation of SIR model parameters through second-order finite differences,” Math. Methods Appl. Sci. 44 (5), 3819–3826 (2021). https://doi.org/10.1002/mma.6985MathSciNetCrossRefMATH

32.

F. Ding, “Combined state and least squares parameter estimation algorithms for dynamic systems,” Appl. Math. Modell. 38 (1), 403–412 (2014). https://doi.org/10.1016/j.apm.2013.06.007MathSciNetCrossRefMATH

33.

A. El Ouissari and K. El Moutaouakil, “Density based fuzzy support vector machine: application to diabetes dataset,” Math. Model. Comput. 8 (4), 747–760 (2021). https://doi.org/10.23939/mmc2021.04.747CrossRef

34.

N. Aharrane, A. Dahmouni, K. El Moutaouakil, and K. Satori, “A robust statistical set of features for Amazigh handwritten characters,” Pattern Recognit. Image Anal. 27 (1), 41–52 (2017). https://doi.org/10.1134/S1054661817010011CrossRef

35.

E. Bas, “A robust optimization approach to diet problem with overall glycemic load as objective function,” Appl. Math. Modell. 38 (19–20), 4926–4940 (2014). https://doi.org/10.1016/j.apm.2014.03.049MathSciNetCrossRefMATH

36.

T. Lind, B. Lönnerdal, H. Stenlund, D. Ismail, R. Seswandhana, E.-C. Ekstrom, and L.-A. Persson, “A community-based randomized controlled trial of iron and zinc supplementation in Indonesian infants: interactions between iron and zinc,” Am. J. Clin. Nutr. 77 (4), 883–890 (2003). https://doi.org/10.1093/ajcn/77.4.883CrossRef

37.

B. L. Specker, A. Beck, H. Kalkwarf, and M. Ho, “Randomized trial of varying mineral intake on total body bone mineral accretion during the first year of life,” Pediatrics 99 (6), e12 (1997). https://doi.org/10.1542/peds.99.6.e12CrossRef

38.

M. Donati, D. Menozzi, C. Zighetti, A. Rosi, A. Zinetti, and F. Scazzina, “Towards a sustainable diet combining economic, environmental and nutritional objectives,” Appetite 106, 48–57 (2016). https://doi.org/10.1016/j.appet.2016.02.151CrossRef

39.

K. El Moutaouakil, M. Cheggour, S. Chellak, and H. Baïzri, (2021, July)., “Metaheuristics optimization algorithm to an optimal Moroccan diet,” in Proc. 2021 7th Annual International Conference on Network and Information Systems for Computers (ICNISC 2021), Guiyang, China, July 23–25, 2021 (IEEE, 2021), pp. 364–369. https://doi.org/10.1109/ICNISC54316.2021.00072

40.

A. You, Dietary Guidelines for Americans (US Department of Health and Human Services and US Department of Agriculture, 7, 2015).

Titel: Intelligent Local Search for an Optimal Control of Diabetic Population Dynamics
verfasst von: El Ouissari Abdellatif
El Moutaouakil Karim
Baïzri Hicham
Chellak Saliha
Publikationsdatum: 01.12.2022
Verlag: Pleiades Publishing
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe 6/2022
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048222060047

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 6/2022

Study of Filtration Processes in a Gas-Hydrate Reservoir Taking into Account Salinity and Solid-Phase Inclusions

Hybrid Model of a Stationary Plasma Thruster Taking into Account the Finite Electron Mass

Efficient Implementation of the Hybrid Large Particle Method

High-Speed Channel Flow Control with Porous Inserts

Simulation of an Air Shock Wave Using the Equations of State for the Jones–Wilkins–Lee Detonation Products

Mathematical Models of Ionization of Air Plasma by Electron Flux

Premium Partner