Calcium signaling is decisive for cellular functions. This calcium random walk stipulates neuronal functions. Calcium concentration could provoke gene transcription, apoptosis, neuronal plasticity, etc. A malformation in calcium could change the neuron's intracellular behavior. Calcium concentration balancing is a complex cellular mechanism. This occurrence can be handled with the Caputo fractional reaction-diffusion equation. In this mathematical modeling, we have included the STIM-Orai mechanism and Endoplasmic Reticulum (ER) flux, Inositol Triphosphate Receptor (IPR), SERCA, plasma membrane flux, voltage-gated calcium entry, and different buffer interactions. A hybrid integral transform and Green's function approach were taken to solve the initial boundary problem. A closed-form solution of a Mittag-Leffler family function plotted using MATLAB software. Different parameters impact changes in the spatiotemporal behavior of the calcium concentration. Specific roles of organelles involved in Alzheimer's disease-affected neurons are computed. Ethylene glycol tetraacetic acid (EGTA), 1,2-bis(o-aminophenoxy)ethane N,N,N,N-tetraacetic acid (BAPTA), and S100B protein effects are also observed. In all simulations, we can say S100B and the STIM-Orai effect cannot be neglected. This model lights up the different approaches for calcium signaling pathway simulation. As a consequence, we determine that a generalized reaction-diffusion approach is a better fit realistic model.

Degeneration of the neurological system linked to cognitive deficits, daily living exercise clutters, and behavioral disturbing impacts may define Alzheimer's disease. Alzheimer's disease research conducted later in life focuses on describing ways for early detection of dementia, a kind of mental disorder. To tailor our care to each patient, we utilized visual cues to determine how they were feeling. We did this by outlining two approaches to diagnosing a person's mental health. Support vector machine is the first technique. Image characteristics are extracted using a fractal model for classification in this method. With this technique, the histogram of a picture is modeled after a Gaussian distribution. Classification was performed with several support vector machines kernels, and the outcomes were compared. Step two proposes using a deep convolutional neural network architecture to identify Alzheimer's-related mental disorders. According to the findings, the support vector machines approach accurately recognized over 93% of the photos tested. The deep convolutional neural network approach was one hundred percent accurate during model training, whereas the support vector machines approach achieved just 93 percent accuracy. In contrast to support vector machines accuracy of 89.3%, the deep convolutional neural network model test findings were accurate 98.8% of the time. Based on the findings reported here, the proposed deep convolutional neural network architecture may be used for diagnostic purposes involving the patient's mental state.

In this paper, a fractional-order coinfection model for the transmission dynamics of COVID-19 and tuberculosis is presented. The positivity and boundedness of the proposed coinfection model are derived. The equilibria and basic reproduction number of the COVID-19 sub-model, Tuberculosis sub-model, and COVID-19 and Tuberculosis coinfection model are derived. The local and global stability of both the COVID-19 and Tuberculosis sub-models are discussed. The equilibria of the coinfection model are locally asymptotically stable under certain conditions. Later, the impact of COVID-19 on TB and TB on COVID-19 is analyzed. Finally, the numerical simulation is carried out to assess the effect of various biological parameters in the transmission dynamics of COVID-19 and Tuberculosis coinfection.

In this article, we present a novel approach under the Fibonacci wavelet and collocation technique which is computationally efficient to obtain the solution of the model of cells of HIV infection. A system of nonlinear ordinary differential equations represents this mathematical model. We have approximated unknown functions and their derivatives using the operational matrix of integration of Fibonacci wavelets to transform this model into a set of algebraic equations and then simplified using a suitable method. It is anticipated that the proposed approach would be more efficient and suitable for solving a variety of nonlinear ordinary and partial differential equations representing the model of medical, radiation, and surgical oncology, and drug targeting systems that occur in medical science and engineering. Tables and graphs are included to show how the suggested wavelet method provides enhanced accuracy for a wide range of problems. Relative data and computations are performed over MATLAB software.

Due to the advanced network technology, there is almost no barrier to information dissemination, which has led to the breeding of rumors. Intended to clarify the dynamic mechanism of rumor propagation, we formulate a SIR model with time delay, forced silence function and forgetting mechanism in both homogeneous and heterogeneous networks. In the homogeneous network model, we first prove the nonnegativity of the solutions. Based on the next-generation matrix, we calculate the basic reproduction number . Besides, we discuss the existence of equilibrium points. Next, by linearizing the system and constructing a Lyapunov function, the local and global asymptotically stability of the equilibrium points are found. In the heterogeneous network model, we derive the basic reproduction number through the analysis of a rumor-prevailing equilibrium point . Moreover, we conduct the local and global asymptotic stability analysis for the equilibrium points according to the LaSalle's Invariance Principle and stability theorem. As long as the maximum spread rate is large enough, the rumor-prevailing point is locally asymptotically stable when . Additionally, it hits that the system exists bifurcation behavior at due to the newly added forced silence function. Later, after adding two controllers to the system, we research the problem of optimal control. Finally, aimed at authenticating the above theoretical results, a serious of numerical simulation experiments are carried out.

The aim of the current study is to investigate the spread of the COVID-19 pandemic as a multiphase percolation process. Mathematical equations have been developed to describe the time dependence of the number of cumulative infected individuals, , and the velocity of the pandemic, , as well as to calculate epidemiological characteristics. The study focuses on the use of sigmoidal growth models to investigate multiwave COVID-19. Hill, logistic dose response and sigmoid Boltzmann models fitted successfully a pandemic wave. The sigmoid Boltzmann model and the dose response model were found to be effective in fitting the cumulative number of COVID-19 cases over time 2 waves spread (N = 2). However, for multiwave spread (N > 2), the dose response model was found to be more suitable due to its ability to overcome convergence issues. The spread of N successive waves has also been described as multiphase percolation with a period of pandemic relaxation between two successive waves.

Air transportation systems are a foundational infrastructure for the human's society. The lack of systematic and detailed investigation on a large amount of records for air flights has blocked seriously the deep understanding of the systems. By using the American domestic passenger flight records from 1995 to 2020, we constructed the air transportation networks and calculated the betweenness and the eigenvector centralities for the airports. It is found that in terms of eigenvector centrality, 15-30% airports in the unweighted and undirected networks behave anomalous. The anomalies disappear after considering the information of link weights or directionalites. Five widely used models for air transportation networks are evaluated, results for which tell us that the spatial constraints are required to eliminate the anomalies detected by the eigenvector centrality, and provide us some references for selecting the parameters in the models. We hope the empirical benchmarks reported in this paper can stimulate much more works on theoretical models for air transportation systems.

COVID-19 is a pandemic disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). This virus is mainly spread by droplets, respiratory secretions, and direct contact. Caused by the huge spread of the COVID-19 epidemic, research is focused on the study of biosensors as it presents a rapid solution for reducing incidents and fatality rates. In this paper, a microchip flow confinement method for the rapid transport of small sample volumes to sensor surfaces is optimized in terms of the confinement coefficient β, the position of the confinement flow X, and its inclination α relative to the main channel. A numerical simulation based on two-dimensional Navier-Stokes equations has been used. Taguchi's L9(33) orthogonal array was adopted to design the numerical assays taking into account the confining flow parameters (α, β, and X) on the response time of microfluidic biosensors. Analyzing the signal-to-noise ratio allowed us to determine the most effective combinations of control parameters for reducing the response time. The contribution of the control factors to the detection time was determined via analysis of variance (ANOVA). Numerical predictive models using multiple linear regression (MLR) and an artificial neural network (ANN) were developed to accurately predict microfluidic biosensor response time. This study concludes that the best combination of control factors is that corresponds to , and X = 40µm. Analysis of variance (ANOVA) shows that the position of the confinement channel (62% contribution) is the factor most responsible for the reduction in response time. Based on the correlation coefficient (R 2), and value adjustment factor (VAF), the ANN model performed better than the MLR model in terms of prediction accuracy.

The current study deals with the stochastic reaction-diffusion epidemic model numerically with two proposed schemes. Such models have many applications in the disease dynamics of wildlife, human life, and others. During the last decade, it is observed that the epidemic models cannot predict the accurate behavior of infectious diseases. The empirical data gained about the spread of the disease shows non-deterministic behavior. It is a strong challenge for researchers to consider stochastic epidemic models. The effect of the stochastic process is analyzed. So, the SIR epidemic model is considered under the influence of the stochastic process. The time noise term is taken as the stochastic source. The coefficient of the stochastic term is a Borel function, and it is used to control the random behavior in the solutions. The proposed stochastic backward Euler scheme and the proposed stochastic implicit finite difference scheme (IFDS) are used for the numerical solution of the underlying model. Both schemes are consistent in the mean square sense. The stability of the schemes is proven with Von-Neumann criteria and schemes are unconditionally stable. The proposed stochastic backward Euler scheme converges toward a disease-free equilibrium and does not converge toward an endemic equilibrium but also possesses negative behavior. The proposed stochastic IFD scheme converges toward disease-free equilibrium and endemic equilibrium. This scheme also preserves positivity. The graphical behavior of the stochastic SIR model is much similar to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The efficacy of the proposed scheme is shown in the graphical behavior of the test problem for the various values of the parameters.

This work investigates the generalised time-fractional Cattaneo model. The homotopy perturbation transform technique is used to get the numerical solution of this model. The stability is analysed using the Lyapunov function, also the error analysis is discussed. Finally, the effectiveness of the proposed technique is illustrated by calculating the and error and comparing it with the existing techniques.