Mathematical Study of A Memory Induced Biochemical System

Mithun Kumar Ghosh; Tridip Sardar; Xianbing Cao; Priti Kumar Roy

doi:10.1109/JAS.2018.7511234

Volume 5 Issue 6

Nov. 2018

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2018 > 5(6): 1142-1149

Mithun Kumar Ghosh, Tridip Sardar, Xianbing Cao and Priti Kumar Roy, "Mathematical Study of A Memory Induced Biochemical System," IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1142-1149, Nov. 2018. doi: 10.1109/JAS.2018.7511234

Citation:

Mithun Kumar Ghosh, Tridip Sardar, Xianbing Cao and Priti Kumar Roy, "Mathematical Study of A Memory Induced Biochemical System," IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1142-1149, Nov. 2018. doi: 10.1109/JAS.2018.7511234

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Mathematical Study of A Memory Induced Biochemical System

doi: 10.1109/JAS.2018.7511234

1.
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
2.
Department of Mathematics, Dinabondhu Andrews College, Kolkata 700084, India
3.
College of Science, Beijing Technology and Business University, Beijing 100037, China

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Author Bio:
Mithun Kumar Ghosh received the B.Sc. and M.Sc. degrees from the University of Calcutta, India, in 2005 and 2007 respectively. He is a member of the Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, India, and is pursuing the Ph.D. degree at the same university. His research interests focus on model formulation, analysis and control of enzymatic reactions

Tridip Sardar graduated from the University of Calcutta, India, in 2006. He received the M.Sc. degree from IIT Kanpur, India, in 2008 and the Ph.D. degree in applied mathematics from the University of Calcutta, India, in 2015. He is currently an Assistant Professor in the Department of Mathematics, Dinabandhu Andrews College, India. His research interests include mathematical epidemiology, non-linear dynamics, application of fractional differential equations

Xianbing Cao received the B.S. degree in mathematics from Jishou University in 1984, the M.S. degree in probability theory from Harbin Institute of Technology in 1990, and his Ph.D. degree in stochastic control theory from the Chinese Academy of Sciences in 2002. He has been a Professor at Beijing Technology and Business University since 2003, and currently is Dean of the School of Science. His research interests include stochastic control systems, system identification and financial time series analysis

Priti Kumar Roy is a Professor of the Department of Mathematics, Jadavpur University. He is proficient in nonlinear system dynamics and an expert in mathematical modeling. He researches infectious diseases like HIV, cutaneous leishmaniasis, filariasis and auto immune disease like psoriasis. Apart from epidemiology, he also researches on industrial mathematics on production of biodiesel from the jatropha curcus plant and its oil production optimization. Furthermore, he also researches the ecological modelling of some important ecological and environmental issues. He has published over 100 peer reviewed publications in international and national journals on his research topics. Prof. Roy edited one book- Insight and Control of Infectious Disease in Global Scenario published by Intech Publishers, and is the author of Springer publication entitled Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission, which is published this year. He has guided 8 Ph.D. students and 8 more scholars are working under his guidance. He is the first person to supervise a thesis on mathematical models of Psoriasis. He is an eminent member of different National and International Societies like Biomathematical Society of India (BMSI), International Association of Engineers (IAENG), European Society of Clinical Microbiology and Infectious Diseases (ESCMID) and European Society for Mathematical and Theoretical Biology (ESMTB). He has completed 6 research projects as Principal Investigator, sponsored by Government of India. Prof. Roy was awarded the Best Paper Award in World Congress on Engineering 2010 held in London, UK. He was selected as an Indian Scientist under the International Collaboration/Exchange Program 2011-2012 and again in 2016 awarded by INSA. He was also awarded with Siksha Ratan award in 2012. Prof. Roy delivered invited lectures in more than 39 overseas Universities, Institutes and numerous lectures in Indian Universities
Corresponding author: Priti Kumar Roy, e-mail:pritiju@gmail.com
Received Date: 2017-06-11
Accepted Date: 2018-03-07

Abstract

Abstract

In this work, to study the effect of memory on a bi-substrate enzyme kinetic reaction, we have introduced an approach to fractionalize the system, considering it as a threecompartmental model. Solutions of the fractionalized system are compared with the corresponding integer-order model. The equilibrium points of the fractionalized system are derived analytically. Their stability properties are discussed from numerical aspect. We determine the changes of the substances due to the changes of "memory effect". The effect is discussed critically from the perspective of product formation. We have also analyzed the memory induced system with a control measure in view of optimizing the product. Our numerical result reveals that the solutions of the fractionalized system, when it is free from memory, are in good agreement with the integer-order system. It is noticed that the effect of memory influences the reaction in the forward direction and assists in yielding the product more quickly. However, an extensive use of memory makes the system slower, but introduction of a control input makes the reaction faster. It is possible to overcome the slowness of the reaction due to the undue effect of memory by appropriate use of a control measure.
- Bi-substrate enzymatic reaction,
- compartmental system,
- control theoretic approach,
- fractional-order differential equations,
- memory effect

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References(39)

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Mathematical Study of A Memory Induced Biochemical System

doi: 10.1109/JAS.2018.7511234

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