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Modeling the mechanics of calcium regulation in T lymphocyte:A finite element method approach

International Journal of Biomathematics 2020年第5期13卷 149-169页

作者： parvaiz ahmad naik School of Mathematics and Statistics Xi'an Jiaotong Unirersity Xi'an Shaanxi 710049P.R.China

Changes in cellular Ca2+concentration control a variety of physiological activities including hormone and neurotransmitter release,muscular contraction,synaptic plas-ticity,ionic channel permeability,apoptosis,enzyme activity,gene transcription and reproduction ***-temporal Ca2+dynamics due to Ca2 t release,buffering and re-uptaking plays a central role in studying the Ca2+regulation in T *** most cases,Ca2+has its major signaling function when it is elevated in the cytosolic *** this paper,a two-dimensional mathematical model to study spatiotemporal variations of intracellular Ca2+concentration in T lymphocyte cell is proposed and *** cell is assumed to be a circular shaped geomnetrical domain for the representation of properties of Ca2+dynamics within the cell includ-ing important ***2+binding proteins for the dynamics of Ca2+are itself buffer and other physiological parameters located in Ca2+*** model incorpo-rates the important biophysical processes like difusion,reaction,voltage gated Ca2+channel,leak from endoplasmic reticulum(ER),efflux from cytosol to ER via sarco ER Ca2+adenosine triphosphate(SERCA)pumps,buffers and Na+/Ca2+*** proposed mathematical model is solved using a finite difference method and the finite element *** initial and boundary conditions are incorporated in the model based on biophysical conditions of the *** simulations in MAT-LAB R2019b are employed to investigate mathematical models of reaction-diffusion *** effect of source,buffer,Nat/Ca2+exchanger,*** spatial and tempo-ral patterns of Ca2+in T lymphocyte has been studied with the help of numerical *** the obtained results,it is observed that,the coordinated combination of the incor-porated parameters plays a significant role in Ca2+regulation in T *** leak and voltage-gated Ca2+channel provides the necessary Ca2+to the cell when required for its proper

关键词： Nat/Ca2+exchanger SERCA purmp ER leak voltage gated Ca2+channel buffers diffusion coefficient reaction-diffusion equations Ritz method and variational form

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Global dynamics of a fractional-order SIR epidemic model with memory

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International Journal of Biomathematics 2020年第8期13卷 1-23页

作者： parvaiz ahmad naik School of Mathematics and Statistics Xi’an Jiaotong University Xi’an Shaanxi 710049P.R.China

In this paper,an investigation and analysis of a nonlinear fractional-order SIR epidemic model with Crowley-Martin type functional response and Holling type-II treatment rate are established along the *** existence and stability of the equilibrium points are *** sufficient conditions for the persistence of the disease are ***,a threshold value,Ro,is obtained which determines the stability of equilibria,then model equilibria are determined and their stability analysis is considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle invariant *** fractional derivative is taken in Caputo sense and the numerical solution of the model is obtained by LI scheme which involves the memory trace that can capture and integrate all past ***,by using Lyapunov functional approach,the global dynamics of the endemic equilibrium point is ***,some numerical simulations are performed to illustrate the effectiveness of the theoretical results *** outcome of the study reveals that the applied LI scheme is computationally very strong and effective to analyze fractional-order differential equations arising in disease *** results show that order of the fractional derivative has a significant effect on the dynamic ***,from the results,it is obvious that the memory effect is zero for p=*** the fractional-order p is decreased from 1,the memory trace nonlinearly increases from 0,and its dynamics strongly depends on *** memory effect points out the difference between the derivatives of the fractional-order and integer order.

关键词： SIR epidemic model Caputo fractional derivative LI scheme memory stability analysis reproduction number Ro

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Stability analysis of a fractional-order cancer model with chaotic dynamics

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International Journal of Biomathematics 2021年第6期14卷 239-261页

作者： parvaiz ahmad naik Jian Zu Mehraj-ud-din naikt School of Mathematics and Statistics Xi’an Jiaotong University Xi’anShaanxi 710049P.R.China Department of Chemical Engineering College of Engineering Jazan UniversityJazan 45142Saudi Arabia

In this paper,we develop a three-dimensional fractional-order cancer *** proposed model involves the interaction among tumor cells,healthy tissue cells and activated effector *** detailed analysis of the equilibrium points is ***,the existence and uniqueness of the solution are *** fractional derivative is considered in the Caputo *** simulations are performed to illustrate the effectiveness of the obtained theoretical *** outcome of the study reveals that the order of the fractional derivative has a significant effect on the dynamic ***,the calculated Lyapunov exponents give the existence of chaotic behavior of the proposed ***,it is observed from the obtained results that decrease in fractional-order p increases the chaotic behavior of the model.

关键词： Cancer model Caputo fractional derivative chaos stability analysis.

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