Abstract
The crucial point of this article is to discuss the application of fuzzy differential equation (FDE) on a biological problem. In this paper, a mathematical modelling for the diffusion of glucose and a typical drug molecule in the blood stream as the fluid connective tissue in human system has been designed and studied in a fuzzy and a heterogeneous environment, in order to understand the biological importance of the diffusion kinetics of the model drug molecule and the secreted glucose molecule from the meal to the blood stream for achieving the drug efficacy of treatment and the resulting glucose distribution in the body. Generalised Hukuhara derivative approach has been envisaged, wherein the mechanism of conversion of the mathematical models into system of crisp differential equations is discussed in details. The stability analysis of the same is performed in a fuzzy uncertain environment elaborately. The numerical solutions of the models are calculated and illustrated in an efficient way using MATLAB for understanding the theoretical basis of the study in details.
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References
Abd-el-Malek, M.B., M.M. Kassem, and M.L.M. Meky. 2002. Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane. Journal of Computation Mathematics 14: 1–11.
Khanday, M.A., and A. Rafiq. 2015. Variational finite element method to study the absorption rate of drug at various compartments through transdermal drug delivery system. Alexandria Journal Medicine 51 (3): 219–223.
Khanday, M.A., and A. Rafiq. 2016. Numerical estimation of drug diffusion at dermal regions of human body in transdermal drug delivery system. Journal of Mechanics in Medicine and Biology 16 (3): 1650022.
Phu, N.D., A. Ahmadian, N.N. Hung, S. Salahshour, and N. Senu. 2019. Narrow metric semi-linear space of intuitionistic fuzzy numbers: Application to AIDS model. International Journal Of fuzzy Systems 21 (6): 1738–1754.
Ahmadian, A., S. Salahshour, C.S. Chan, and D. Baleanu. 2018. Numerical solutions of fuzzy differential equations by an efficient Runge-Kutta method with generalized differentiability. Fuzzy Sets and Systems 331: 47–67.
Chakraborty, A., S.P. Mondal, A. Mahata, and S. Alam. 2021. Different linear and non-linear form of trapezoidal neutrosophic numbers, de-neutrosophication techniques and its application in time-cost optimization technique, sequencing problem. RAIRO Operations Research 55: S97–S118.
Salahshour, S., A. Ahmadian, A. Mahata, S.P. Mondal, and S. Alam. 2018. The behavior of logistic equation with alley effect in fuzzy environment: Fuzzy differential equation approach. International Journal of Applied and computational Mathematics 4 (2): 62.
Zadeh, L.A. 1965. Fuzzy sets. Information and Control 8: 338–353.
Pal, D., and G.S. Mahapatra. 2015. Dynamic behavior of a predator–prey system of combined harvesting with interval-valued rate parameters. Nonlinear Dynamics. https://doi.org/10.1007/s11071-015-2469-3.
Mahata, A., S.P. Mondal, A. Ahmadian, F. Ismail, S. Alam, and S. Salahshour. 2018. Different solution strategy for solving epidemic model in imprecise environment. Complexity 4902142: 18.
Mahata, A., S.P. Mondal, B. Roy, and S. Alam. 2021. Study of two species prey-predator model in imprecise environment with MSY policy under different harvesting scenario. Environment, Development and Sustainability. https://doi.org/10.1007/s10668-021-01279-2.
Bassanezi, R.C., L.C. de Barros, and P.A. Tonelli. 2000. Attractors and asymptotic stability for fuzzy dynamical systems. Fuzzy Sets and Systems 113: 473–483.
Bede, B., and S.G. Gal. 2010. Solutions of fuzzy differential equations based on generalized differentiability. Communications in Mathematical Analysis 9 (2): 22–41.
Nieto, J.J., A. Khastan, and K. Ivaz. 2009. Numerical solution of fuzzy differential equations under generalized differentiability. Nonlinear Analysis: Hybrid System 3: 700–707.
Das, S., P. Mahato, S.K. Mahato. 2020. A prey predator model in case of disease transmission via pest in uncertain environment. Differential Equation and Dynamical System. https://doi.org/10.1007/s12591-020-00551-7.
Mahata, A., B. Roy, S.P. Mondal, and S. Alam. 2017. Application of ordinary differential equation in glucose-insulin regulatory system modeling in fuzzy environment. Ecological Genetics and Genomics 3–5: 60–66.
Allahviranloo, T., and S. Salahshour. 2011. Euler method for solving hybrid fuzzy differential equation. Soft Computing 15: 1247–1253.
Mahata, A., S.P. Mondal, S. Alam, A. Chakraborty, S.K. Dey, and A. Goswami. 2018. Mathematical model for diabetes in fuzzy environment. Journal of Intelligent and Fuzzy Systems. https://doi.org/10.3233/JIFS-171571.
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Matia, S.N., Mahata, A., Alam, S., Roy, B., Manna, B. (2022). Glucose Distribution and Drug Diffusion Mechanism in the Fuzzy Fluid Connective Tissue in Human Systems: A Mathematical Modelling Approach. In: Peng, SL., Lin, CK., Pal, S. (eds) Proceedings of 2nd International Conference on Mathematical Modeling and Computational Science. Advances in Intelligent Systems and Computing, vol 1422. Springer, Singapore. https://doi.org/10.1007/978-981-19-0182-9_18
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DOI: https://doi.org/10.1007/978-981-19-0182-9_18
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