Memory Effects in the Glycolysis Pathway: Stability, Bifurcations, and Numerical Simulations

The socio-economic burdens of onchocerciasis have prompted the formulation of several mathematical models to better comprehend the epidemic. However, existing models either use integer-order derivatives, which often do not capture the memory and non-local effects seen in infectious diseases, or fractional order with singularity kernels, which may inadequately represent memory effects due to their singularity kernels. Onchocerciasis has a prolonged incubation and slow progression, making past conditions impactful on the disease's current and future course. Fractional derivatives effectively capture this memory effect, providing a more realistic depiction of the infection dynamics than integer-order models. We propose a non-local, non-singular exponential kernel fractional-order onchocerciasis model in the Caputo-Fabrizio fractional derivative sense to capture the disease's memory effects. Our model incorporates early treatment of exposed individuals as a critical intervention parameter, and vector management strategies are also incorporated. Using fixed-point theorem and iterative methods, we establish the existence and uniqueness of solutions, derive conditions for onchocerciasis-free and endemic equilibrium points, and analyze their stability, confirming the model's biological feasibility. Numerical simulations are conducted using a three-step fractional Adams-Bashforth method. Sensitivity analyses indicate that vector management and early treatment effectively reduce the effective reproduction number, while increases in the human-to-vector contact rate elevate it. Numerical results demonstrate that early treatment and vector management can significantly control onchocerciasis. The fractional-order "memory effect" highlights the importance of continuous monitoring and consistent application of control measures to reduce the memory index and curb onchocerciasis prevalence over time.

Untangling the memory and inhibitory effects on SIS-epidemic model with Beddington–DeAngelis infection rate

The memory effect has seen a surge of research into its fundamental properties and applications since its discovery by Feng et al. [Phys. Rev. Lett. 61, 834 (1988)]. While the wave trajectories for which the memory effect holds are hidden implicitly in the diffusion probability function [Phys. Rev. B 40, 737 (1989)], the physical intuition of why these trajectories satisfy the memory effect has often been masked by the derivation of the memory correlation function itself. In this paper, we explicitly derive the specific trajectories through a random medium for which the memory effect holds. Our approach shows that the memory effect follows from a simple conservation argument, which imposes geometrical constraints on the random trajectories that contribute to the memory effect. We illustrate the time-domain effects of these geometrical constraints with numerical simulations of pulse transmission through a random medium. The results of our derivation and numerical simulations are consistent with established theory and experimentation.

Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect

Demand elasticity is the sensitivity of changes in the number of goods demanded by consumers due to changes in the price of goods. This paper compares the price elasticity of demand with and without memory effect using fractional-order derivatives. This study is designed using the development theory of fractional derivatives for the economic field in determining the price elasticity of demand. The result of numerical simulation using the value of α and p indicated that the price elasticity of demand with memory effect is more accurate than without the memory effect. Furthermore, this study concluded that the price elasticity of demand does not only depend on the latest price (current price) but changes in all prices from a specific time interval. The findings of this study suggest future studies can examine the phenomenon of market equilibrium using fractional-order derivatives.

The radial distribution functions of randomly distributed one-dimensional spheres are studied. The differences between equilibrium fluids and sequentially constructed systems are discussed in terms of the corresponding configuration spaces and numerical simulations. It is shown that for the sequentially constructed systems, which correspond to the car parking problem, a 'memory effect' occurs, such that the sequential spheres are temporally distinguishable. Exact solutions for some simple cases and numerical simulations for large systems are shown, discussed and compared with the equilibrium fluid results.

New feedback control for a novel two-dimensional lattice hydrodynamic model considering driver’s memory effect

The dynamics of ionization waves (IWs) in atmospheric pressure discharges is fundamentally determined by the electric polarity (positive or negative) at which they are generated and by the presence of memory effects, i.e. leftover charges and reactive species that influence subsequent IWs. This work examines and compares positive and negative IWs in pulsed plasma jets (1 upmu s on-time), showing the difference in their nature and the different resulting interaction with a dielectric BSO target. For the first time, it is shown that a surface charging memory effect is produced, i.e. that a significant amount of surface charges and electric field remain in the target in between discharge pulses (200 upmu s off-time). This memory effect directly impacts IW dynamics and is especially important when using negative electric polarity. The results suggest that the remainder of surface charges is due to the lack of charged particles in the plasma near the target, which avoids a full neutralization of the target. This demonstration and the quantification of the memory effect are possible for the first time by using an unique approach, assessing the electric field inside a dielectric material through the combination of an advanced experimental technique called Mueller polarimetry and state-of-the-art numerical simulations.

Modeling and simulation of traffic flow based on memory effect and driver characteristics

Scattering in medium is a serious problem that limits the imaging depth or imaging distance. According to the absorption and scattering of light in biological tissues, it is difficult for both excited light and signal light to penetrate biological tissues, and the scattering effect in biological tissues will destroy the phase information of signal light, so it is difficult to directly carry out high resolution imaging in deep biological tissues. In the recent studies it is surprisingly found that two-dimensional image information of an object can be directly recovered from the disordered speckle pattern with pseudothermal light sources based on the optical memory effect (ME) and autocorrelation (AC) method. In this paper, we study a speckle imaging method based on pseudothermal illumination, where the Gerchberg-Saxton algorithm is used to perform the phase recovery of the object. Here, the advantages and disadvantages of HIO&ER algorithm and ping-pang (PP) algorithm based on the ME and AC method for imaging through random scattering medium are compared by using numerical simulation. By comparing the recovery effects and the numbers of iterations between HIO&ER algorithm and PP algorithm, it is found that PP algorithm has a fast running speed when a higher recovery quality is maintained. In addition, a continuous He-Ne laser and rotating ground glass are used to produce a pseudothermal light source. And a single frame imaging of different shape objects, which are a few millimeters away from random scattering medium, is carried out by objective lens. Then PP algorithm is adopted to recover the actual image of micron object. Furthermore, we experimentally find that the magnification, resolution and image intensity, which are qualitatively studied, are seriously affected by the distance between the focal plane of the object lens and scattering medium. We find that with the increase of the distance, the obtained autocorrelation graph and retrieval graph have corresponding amplification and the object sampling point information collected on sCOMS increases, which improves its resolution. However, the scattered light intensity collected by objective lens decreases after passing through the scattering medium, making the intensity of recovered image weaken. The results of this study will further promote the application of ME and AC method in the study of deep tissue medical imaging.

Analysis and achievement for fractional optimal control of Hepatitis B with Caputo operator

TIGAR is a p53 inducible gene that triggers changes in glycolytic metabolic pathway states. It is known that TIGAR expression lowers the fructose - 2, 6-bisphosphate levels resulting in an inhibition of glycolysis and decrease in intracellular ROS levels. Therefore, it is interesting to document data on p53 induced TIGAR protein 2 in the glycolytic pathway. We describe a two-oscillator model consisting of the p53-Mdm2 network and glycolytic pathway with the TIGAR protein. The numerical simulation of the model shows the suppression of glycolytic oscillation as the level of TIGAR protein increases in agreement with the experimental results reported. Thus, stochastic simulation data helps to understand the realistic behaviour in the pathway.

Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our Universe.

Gravitational memory effects are predictions of general relativity that are characterized by an observable effect that persists after the passage of gravitational waves. In recent years, they have garnered particular interest, both due to their connection to asymptotic symmetries and soft theorems and because their observation would serve as a unique test of the nonlinear nature of general relativity. Apart from the more commonly known displacement and spin memories, however, there are other memory effects predicted by Einstein’s equations that are associated with more subleading terms in the asymptotic expansion of the Bondi-Sachs metric. In this paper, we write explicit expressions for these higher memory effects in terms of their charge and flux contributions. Further, by using a numerical relativity simulation of a binary black hole merger, we compute the magnitude and morphology of these terms and compare them to those of the displacement and spin memory. We find that, although these terms are interesting from a theoretical perspective, due to their small magnitude they will be particularly challenging to observe with current and future detectors.

We study the dynamics of the pattern formation in a class of adsorption/desorption systems described by the reaction-Cattaneo model (with memory effects of the diffusion flux). It is shown that pattern selection processes are realized in such systems due to the memory effects. We found that the oscillatory behavior of the radius of the adsorbate islands is governed by the finite propagation speed. The oscillatory dynamics of the pattern formation are studied in detail by numerical simulations.