scholarly journals A Numerical Comparison for a Discrete HIV Infection of CD4+T-Cell Model Derived from Nonstandard Numerical Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mevlüde Yakıt Ongun ◽  
İlkem Turhan
Keyword(s):  
Asymptotic Stability ◽  
Hiv Infection ◽  
Numerical Scheme ◽  
Cell Model ◽  
Continuous Model ◽  
Numerical Comparison ◽  
Time Model ◽  
Stability Properties ◽  
Local Asymptotic Stability ◽  
Linearized Stability

A nonstandard numerical scheme has been constructed and analyzed for a mathematical model that describes HIV infection of CD4+T cells. This new discrete system has the same stability properties as the continuous model and, particularly, it preserves the same local asymptotic stability properties. Linearized Stability Theory and Schur-Cohn criteria are used for local asymptotic stability of this discrete time model. This proposed nonstandard numerical scheme is compared with the classical explicit Euler and fourth order Runge-Kutta methods. To show the efficiency of this numerical scheme, the simulated results are given in tables and figures.

Stability, bifurcation analysis and chaos control for a predator-prey system

2018 ◽  
Vol 25 (3) ◽  
pp. 612-626 ◽  
Author(s):  
Qamar Din
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Chaos Control ◽  
Period Doubling ◽  
Qualitative Behavior ◽  
Time Model ◽  
Center Manifold Theorem ◽  
Stability Of Equilibria ◽  
Local Asymptotic Stability ◽  
Predator Model

We study qualitative behavior of a modified prey–predator model by introducing density-dependent per capita growth rates and a Holling type II functional response. Positivity of solutions, boundedness and local asymptotic stability of equilibria were investigated for continuous type of the prey–predator system. In order to discuss the rich dynamics of the proposed model, a piecewise constant argument was implemented to obtain a discrete counterpart of the continuous system. Moreover, in the case of a discrete-time prey–predator model, the boundedness of solutions and local asymptotic stability of equilibria were investigated. With the help of the center manifold theorem and bifurcation theory, we investigated whether a discrete-time model undergoes period-doubling and Neimark–Sacker bifurcation at its positive steady-state. Finally, two novel generalized hybrid feedback control methods are presented for chaos control under the influence of period-doubling and Neimark–Sacker bifurcations. In order to illustrate the effectiveness of the proposed control strategies, numerical simulations are presented.

scholarly journals Qualitative Properties of Autocatalytic Reactions Occurring in a Flow System

1985 ◽  
Vol 40 (7) ◽  
pp. 736-747
Author(s):  
Sang H. Kim ◽  
Vladimir Hlavacek
Keyword(s):  
Chaotic Behavior ◽  
Flow System ◽  
Cell Model ◽  
Dispersion Model ◽  
Travelling Waves ◽  
Continuous Model ◽  
Product Inhibition ◽  
Stable Node ◽  
Qualitative Properties ◽  
Intermediate Value

The dynamic behavior of an autocatalytic reaction with a product inhibition term is studied in a flow system. A unique steady state exists in the continuous tank reactor. Linear stability analysis predicts either a stable node, a focus or an unstable saddle-focus. Sustained oscillations around the unstable focus can occur for high values of the Damköhler number (Da). In the distributed system, travelling, standing or complex oscillatory waves are detected. For a low value of Da, travelling waves with a pseudo-constant pattern are observed. With an intermediate value of Da, single or multiple standing waves are obtained. The temporal behavior indicates also the appearance of retriggering or echo waves. For a high value of Da, both single peak and complex multipeak oscillations are found. In the cell model, both regular oscillations near the inlet and chaotic behavior downstream are observed. In the dispersion model, higher Peclet numbers (Pe) eliminate the oscillations. The spatial profile shows a train of pulsating waves for the discrete model and a single pulsating or solitary wave for the continuous model.

Model-Based Discrete Linear State Estimator for Nonlinearizable Systems With State-Dependent Noise

1990 ◽  
Vol 112 (4) ◽  
pp. 774-781 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Discrete Time ◽  
Continuous Model ◽  
Equivalent Model ◽  
State Estimator ◽  
Time Model ◽  
State Dependent ◽  
Present Technique ◽  
Linear State ◽  
Noisy Measurement ◽  
Time Linear

A practical technique to derive a discrete-time linear state estimator for estimating the states of a nonlinearizable stochastic system involving both state-dependent and external noises through a linear noisy measurement system is presented. The present technique for synthesizing a discrete-time linear state estimator is first to construct an equivalent reference linear model for the nonlinearizable system such that the equivalent model will provide the same stationary covariance response as that of the nonlinear system. From the linear continuous model, a discrete-time state estimator can be directly derived from the corresponding discrete-time model. The synthesizing technique and filtering performance are illustrated and simulated by selecting linear, linearizable, and nonlinearizable systems with state-dependent noise.

Local asymptotic stability for dissipative wave systems

1998 ◽  
Vol 104 (1) ◽  
pp. 29-50 ◽  
Author(s):  
Patrizia Pucci ◽  
James Serrin
Keyword(s):  
Asymptotic Stability ◽  
Local Asymptotic Stability

Modeling short-term interval-force relations in cardiac muscle

2000 ◽  
Vol 278 (3) ◽  
pp. H913-H931 ◽  
Author(s):  
J. Jeremy Rice ◽  
M. Saleet Jafri ◽  
Raimond L. Winslow
Keyword(s):  
Ryanodine Receptor ◽  
Cell Model ◽  
Isometric Force ◽  
Delayed Rectifier ◽  
Short Term ◽  
Time Model ◽  
Receptor Adaptation ◽  
Myofilament Activation ◽  
Recirculation Fraction ◽  
Ventricular Cell Model

This study employs two modeling approaches to investigate short-term interval-force relations. The first approach is to develop a low-order, discrete-time model of excitation-contraction coupling to determine which parameter combinations produce the degree of postextrasystolic potentiation seen experimentally. Potentiation is found to increase 1) for low recirculation fraction, 2) for high releasable fraction, i.e., the maximum fraction of Ca2+released from the sarcoplasmic reticulum (SR) given full restitution, and 3) for strong negative feedback of the SR release on sarcolemmal Ca2+ influx. The second modeling approach is to develop a more detailed single ventricular cell model that simulates action potentials, Ca2+-handling mechanisms, and isometric force generation by the myofilaments. A slow transition from the adapted state of the ryanodine receptor produces a gradual recovery of the SR release and restitution behavior. For potentiation, a small extrasystolic release leaves more Ca2+ in the SR but also increases the SR loading by two mechanisms: 1) less Ca2+-induced inactivation of L-type channels and 2) reduction of action potential height by residual activation of the time-dependent delayed rectifier K+ current, which increases Ca2+ influx. The cooperativity of the myofilaments amplifies the relatively small changes in the Ca2+ transient amplitude to produce larger changes in isometric force. These findings suggest that short-term interval-force relations result mainly from the interplay of the ryanodine receptor adaptation and the SR Ca2+ loading, with additional contributions from membrane currents and myofilament activation.

scholarly journals Mathematical Analysis of an Immune-structured Hikungunya Transmission Model

2019 ◽  
Vol 12 (4) ◽  
pp. 1533-1552
Author(s):  
Kambire Famane ◽  
Gouba Elisée ◽  
Tao Sadou ◽  
Blaise Some
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Transmission Model ◽  
Acquired Immunity ◽  
Local Asymptotic Stability ◽  
Well Posed ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, itappears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the diseasefree equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

scholarly journals Trans cohort metabolic reprogramming towards glutaminolysis in long-term successfully treated HIV-infection

2022 ◽  
Vol 5 (1) ◽  
Author(s):  
Flora Mikaeloff ◽  
Sara Svensson Akusjärvi ◽  
George Mondinde Ikomey ◽  
Shuba Krishnan ◽  
Maike Sperk ◽  
...  
Keyword(s):  
Hiv Infection ◽  
Cell Model ◽  
Antiretroviral Drugs ◽  
Metabolic Reprogramming ◽  
System Level ◽  
People Living With Hiv ◽  
Low Grade ◽  
Middle Income ◽  
Living With Hiv

AbstractDespite successful combination antiretroviral therapy (cART), persistent low-grade immune activation together with inflammation and toxic antiretroviral drugs can lead to long-lasting metabolic flexibility and adaptation in people living with HIV (PLWH). Our study investigated alterations in the plasma metabolic profiles by comparing PLWH on long-term cART(>5 years) and matched HIV-negative controls (HC) in two cohorts from low- and middle-income countries (LMIC), Cameroon, and India, respectively, to understand the system-level dysregulation in HIV-infection. Using untargeted and targeted LC-MS/MS-based metabolic profiling and applying advanced system biology methods, an altered amino acid metabolism, more specifically to glutaminolysis in PLWH than HC were reported. A significantly lower level of neurosteroids was observed in both cohorts and could potentiate neurological impairments in PLWH. Further, modulation of cellular glutaminolysis promoted increased cell death and latency reversal in pre-monocytic HIV-1 latent cell model U1, which may be essential for the clearance of the inducible reservoir in HIV-integrated cells.

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