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Stability analysis of drugdynamics model: A mat hematical approach

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International Journal of Biomathematics 2019年第4期12卷 153-184页

作者： koyel Chakravarty D.C.Dalal Department of Mathematics Indian Institute of Technology Guwahati Guwahati 781039 India Faculty of Science and Technology ICFAI University TripuraTripura 799210India

In this paper, a mathematical model of drug release from polymeric matrix and consequent intracellular drug transport is proposed and analyzed. Modeling of drug release is done through solubilization dynamics of drug particles, diffusion of the solubilized drug through the polymeric matrix in addition to reversible dissociation/recrystallization process. The interaction between drug-receptor, drug-plasma proteins along with other intracellular endosomal events is modeled. This leads to a mixed system of partial and ordinary differential equations with associated pertinent set of initial and boundary conditions. Furthermore, besides the stability of the proposed model, several sub-models are also studied for their stability criteria. Prominence is provided to the reduced model system having requisite relevance to the original system where quasi steady state approximation (QSSA) theory is utilized. For the model to be potent enough to generate appropriate predictive results for drug delivery, the stability properties of equilibrium in the mathematical model are analyzed both analytically and numerically. Numerical simulation in the embodiment of graphical representations speaks about various vital characteristics of the underlying physical phenomena along with the importance and sensitized impact of the model parameters controlling significant biological functions. Probed new therapies and clinical procedures could be assessed considering the present mathematical model and its analysis as the basis framework in order to effectively enhance therapeutic efficacy and improved patient compliance. The present study confirms the necessity of stability analysis study so that advocated mathematical model can effectively complement the real physiological behavior of pharmacokinetics.

关键词： Mathematical model drug polymeric matrix endosomal events quasi steady state approximation (QSSA) stability

An analytical study of drug release kinetics from a degradable polymeric matrix

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International Journal of Biomathematics 2018年第1期11卷 255-277页

作者： koyel Chakravarty D. C. Dalal Department of MathematicsIndian Institute of Technology Guwahati Guwahati 781039 India

In modern days, biodegradable polymeric matrix used as the kingpin of local drug delivery system is in the center of attention. This work is concentrated on the formulation of mathematical model elucidating degradation of drug-loaded polymeric matrix followed by drug release to the adjacent biological tissues. Polymeric degradation is penciled with mass conservation equations. Drug release phenomenon is modeled by considering solubilization dynamics of drug particles, diffusion of the solubilized drug through polymeric matrix along with reversible dissociation/recrystallization process. In the tissue phase, reversible dissociation/association along with internalization processes of drug are taken into account. For this, a two-phase spatio-temporal model is postulated, which has ensued to a system of partial differential equations. They are solved analytically with appropriate choice of initial, interface and boundary conditions. In order to reflect the potency of the advocated model, the simulated results are analogized with corresponding experimental data and found laudable agreement so as to validate the applicability of the model considered. This model seems to foster the delicacy of the mantle enacted by important drug kinetic parameters such as diffusion coefficients, mass transfer coefficients, particle binding and internalization parameters, which is illustrated through local sensitivity analysis.

关键词：动力学建模聚合矩阵版本数学模型微分方程再结晶过程边界条件

Technology Landscape for Epidemiological Prediction and Diagnosis of COVID-19

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Computers, Materials & Continua 2021年第5期67卷 1679-1696页

作者： Siddhant Banyal Rinky Dwivedi koyel Datta Gupta Deepak Kumar Sharma Fadi Al-Turjman Leonardo Mostarda Department of Instrumentation and Control Netaji Subhas University of TechnologyNew Delhi110078India Department of Computer Science&Engineering Maharaja Surajmal Institute of TechnologyNew Delhi110058India Department of Information Technology Netaji Subhas University of TechnologyNew Delhi110078India Research Center for AI and IoT Near East UniversityNicosiaMersin10Turkey Computer Science Department Camerino UniversityCamerino62032Italy

The COVID-19 outbreak initiated from the Chinese city of Wuhanand eventually affected almost every nation around the globe. From China,the disease started spreading to the rest of the world. After China, Italybecame the next epicentre of the virus and witnessed a very high death *** nations like the USA became severely hit by SARS-CoV-2 virus. TheWorld Health Organisation, on 11th March 2020, declared COVID-19 a pandemic. To combat the epidemic, the nations from every corner of the worldhas instituted various policies like physical distancing, isolation of infectedpopulation and researching on the potential vaccine of SARS-CoV-2. Toidentify the impact of various policies implemented by the affected countrieson the pandemic spread, a myriad of AI-based models have been presented toanalyse and predict the epidemiological trends of COVID-19. In this work, theauthors present a detailed study of different articial intelligence frameworksapplied for predictive analysis of COVID-19 patient record. The forecastingmodels acquire information from records to detect the pandemic spreadingand thus enabling an opportunity to take immediate actions to reduce thespread of the virus. This paper addresses the research issues and correspondingsolutions associated with the prediction and detection of infectious diseaseslike COVID-19. It further focuses on the study of vaccinations to cope withthe pandemic. Finally, the research challenges in terms of data availability,reliability, the accuracy of the existing prediction models and other open issuesare discussed to outline the future course of this study.

关键词： COVID-19 diagnosis deep learning forecasting models machine learning metaheuristics prediction big data pandemic

Biological Evolution: Entropy, Complexity and Stability

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Journal of Modern Physics 2011年第6期2卷 621-626页

作者： C.G Chakrabarti koyel Ghosh 不详

In the present paper we have made an attempt to investigate the importance of the concepts of dynamical stability and complexity along with their interelationship in an evolving biological systems described by a system of kinetic (both deterministic and chaotic) equations. The key to the investigation lies in the expres-sion of a time-dependent Boltzmann-like entropy function derived from the dynamical model of the system. A significant result is the determination of the expression of Boltzmann - entropy production rate of the evolving system leading to the well-known Pesin-type identity which provides an elegant and simple meas-ure of dynamical complexity in terms of positive Lyapunov exponents. The expression of dynamical com-plexity has been found to be very suitable in the study of the increase of dynamical complexity with the suc-cessive instabilities resulting from the appearance of new polymer species (or ecological species) into the original system. The increase of the dynamical complexity with the evolutionary process has been explained with a simple competitive model system leading to the “principle of natural selection”.

关键词： Boltzmann-Entropy Dynamical Stability Pesin-type Identity and Dynamical Complexity Lyapunov Exponents Structural Instabilities Biological Evolution