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The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model's estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations. [ABSTRACT FROM AUTHOR]

In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies. [ABSTRACT FROM AUTHOR]

Recurrent Neural Networks (RNNs), a type of machine learning technique, have recently drawn a lot of interest in numerous fields, including epidemiology. Implementing public health interventions in the field of epidemiology depends on efficient modeling and outbreak prediction. Because RNNs can capture sequential dependencies in data, they have become highly effective tools in this field. In this paper, the use of RNNs in epidemic modeling is examined, with a focus on the extent to which they can handle the inherent temporal dynamics in the spread of diseases. The mathematical representation of epidemics requires taking time-dependent variables into account, such as the rate at which infections spread and the long-term effects of interventions. The goal of this study is to use an intelligent computing solution based on RNNs to provide numerical performances and interpretations for the SEIR nonlinear system based on the propagation of the Zika virus (SEIRS-PZV) model. The four patient dynamics, namely susceptible patients S(y), exposed patients admitted in a hospital E(y), the fraction of infective individuals I(y), and recovered patients R(y), are represented by the epidemic version of the nonlinear system, or the SEIR model. SEIRS-PZV is represented by ordinary differential equations (ODEs), which are then solved by the Adams method using the Mathematica software to generate a dataset. The dataset was used as an output for the RNN to train the model and examine results such as regressions, correlations, error histograms, etc. For RNN, we used 100% to train the model with 15 hidden layers and a delay of 2 seconds. The input for the RNN is a time series sequence from 0 to 5, with a step size of 0.05. In the end, we compared the approximated solution with the exact solution by plotting them on the same graph and generating the absolute error plot for each of the 4 cases of SEIRS-PZV. Predictions made by the model appeared to be become more accurate when the mean squared error (MSE) decreased. An increased fit to the observed data was suggested by this decrease in the MSE, which suggested that the variance between the model's predicted values and the actual values was dropping. A minimal absolute error almost equal to zero was obtained, which further supports the usefulness of the suggested strategy. A small absolute error shows the degree to which the model's predictions matches the ground truth values, thus indicating the level of accuracy and precision for the model's output. [ABSTRACT FROM AUTHOR]

The focus of this work is on the absolute controllability of Hilfer impulsive non-instantaneous neutral derivative (HINND) with integral boundary condition of any order. Total controllability refers to the system's ability to be controlled during the impulse time. Kuratowski measure and semigroup theory in Banach space yield the results. Furthermore, we talked about optimal controllability in conjunction with appropriate limitations. Our established outcomes are described using an example. [ABSTRACT FROM AUTHOR]

Alzheimer's disease stands as one of the most widespread neurodegenerative conditions associated with aging, giving rise to dementia and posing significant public health challenges. Mathematical models are considered as valuable tools to gain insights into the mechanisms underlying the onset, progression, and potential therapeutic approaches for AD. In this paper, we introduce a mathematical model for AD that employs the fractal fractional operator in the Caputo sense to characterize the temporal dynamics of key cell populations. This model encompasses essential elements, including amyloid- β ( A β ), neurons, astroglia and microglia. Using the fractal fractional operator, we have established the existence and uniqueness of solutions for the model under consideration, employing Leray-Schaefer's theorem and the Banach fixed-point methods. Utilizing functional techniques, we have analyzed the proposed model stability under the Ulam-Hyers condition. The suggested model has been numerically simulated by using a fractional Adams-Bashforth approach, which involves a two-step Lagrange polynomial. For numerical simulations, different ranges of fractional order values and fractal dimensions are considered. This new fractal fractional operator in the form of the Caputo derivative was determined to yield better results than an ordinary integer order. Various outcomes are shown graphically by for different fractal dimensions and arbitrary orders. [ABSTRACT FROM AUTHOR]

This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible S (t) , infected I (t) , treated T (t) , and recovered R (t) with the susceptible category further divided into two subcategories S 1 (t) and S 2 (t) . In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner. [ABSTRACT FROM AUTHOR]

Artificial neural networks (ANNs) have transformed machine learning and computational intelligence by providing unprecedented powers in modeling complicated data and addressing a wide range of challenges. In the field of ANNs, back propagation is a key approach for training neural networks. However, obtaining optimum network efficiency while tackling over fitting and controlling uncertainty is a difficult task. The present study employs the Bayesian Regularization Method with Neural Network Backpropagation (BRM-NNB) technique to investigate the rumors spreading delay model. With their rapid spread, rumors have the potential to cause fear and even financial loss. Thus, we must take decisive actions to stop the rumor from spreading. Nowadays, rumors can spread through instant messaging, emails, or publishing, thanks to the development of the internet. In this research, an XY-SIR rumors spreading delay model (XY-SIR-RS-DM) is investigated in relation to the novel spreading pattern. Media networks can be categorized into susceptible and infected media, while friendship networks can be categorized into three groups: spreaders (S, I, and R), who actively disseminate rumors, those who are ignorant and those who have no desire to do so. To estimate the solution of the suggested model, the Bayesian regularization method with neural network back propagation (BRM-NNB) is used. The data set is generated by applying the explicit Runge-Kutta method. The computing BRM-NNB strategy is implemented for three different performances, where the training, testing, and verification data are reported as 80%, 15%, and 5%, respectively, with 10 hidden neurons. To verify the validity of the developed artificial intelligence (AI) approach represented by the BRM-NNB, outcome comparisons are presented. The result is compatible with obtaining a minimal absolute error that is nearly equal to zero, thereby proving the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

The Rastall–Rainbow gravity theory has recently been proposed as a combination of the Rastall and rainbow theories. This theory can be thought as a generalization of the Rastall gravity to an energy dependent Rastall theory, and leads to an additional degrees of freedom. In this paper, we construct models that admit the wormhole geometries within this theory. We analyze the properties of static wormholes based on the profiles of dark matter halos, which was demonstrated earlier in Rahaman et al. (Eur Phys J C 74:2750, 2014) that galactic halo possesses the necessary properties in favour of the existence of wormholes. The main properties are being analyzed by considering three different kinds of halo density profiles. Our results indicate that such wormholes could potentially exist but the NEC is violated in the vicinity of the wormhole throat. We have further examined the stability of the configuration through the adiabatic sound velocity. [ABSTRACT FROM AUTHOR]

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

The cultivation of grapes encounters various challenges, such as the presence of pests and diseases, which have the potential to considerably diminish agricultural productivity. Plant diseases pose a significant impediment, resulting in diminished agricultural productivity and economic setbacks, thereby affecting the quality of crop yields. Hence, the precise and timely identification of plant diseases holds significant importance. This study employs a Convolutional neural network (CNN) with and without data augmentation, in addition to a DCNN Classifier model based on VGG16, to classify grape leaf diseases. A publicly available dataset is utilized for the purpose of investigating diseases affecting grape leaves. The DCNN Classifier Model successfully utilizes the strengths of the VGG16 model and modifies it by incorporating supplementary layers to enhance its performance and ability to generalize. Systematic evaluation of metrics, such as accuracy and F1-score, is performed. With training and test accuracy rates of 99.18 and 99.06%, respectively, the DCNN Classifier model does a better job than the CNN models used in this investigation. The findings demonstrate that the DCNN Classifier model, utilizing the VGG16 architecture and incorporating three supplementary CNN layers, exhibits superior performance. Also, the fact that the DCNN Classifier model works well as a decision support system for farmers is shown by the fact that it can quickly and accurately identify grape diseases, making it easier to take steps to stop them. The results of this study provide support for the reliability of the DCNN classifier model and its potential utility in the field of agriculture. [ABSTRACT FROM AUTHOR]

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas" published in Scientific Reports. The correction addresses an error in the affiliation of one of the authors. The correct affiliation is listed as the Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia. The original article has been corrected. The authors of the article are Yuanyuan Liu, Jalil Manafian, Gurpreet Singh, Naief Alabed Alkader, and Kottakkaran Sooppy Nisar. [Extracted from the article]

SnO 2 quantum dots interspersed Bi 2 WO 6 nanoflowers were successfully synthesized to create a cost-efficient electrode material specifically designed for energy storage devices. The performance of the electrodes was evaluated by studying their structural and functional properties. The SnO 2 quantum dots coupled with Bi 2 WO 6 nanoflowers-based electrodes exhibited an enhanced electrochemical behavior compared to those without the SnO 2. A functional investigation of the developed electrodes in a 3 M KOH electrolyte demonstrated specific capacitance values of 812 and 741 F.g−1 (225.5 and 206 mAh.g−1) for SnO 2 -Bi 2 WO 6 (BWSq) and Bi 2 WO 6 (BW) nanoflowers, respectively, at a current density of 7 A.g−1. Excellent cycling stability was observed for both BWSq and BW electrodes, with specific capacity values of 226 and 159 mAh.g−1 (814 and 572 F.g−1), respectively, after 3000 cycles at a current density of 22 A.g−1. The fabricated BWSq symmetric super-capacitor (SSC) device demonstrated a superior performance with an exceptional specific capacitance of 75.6 F.g−1 when subjected to a current density of 0.5 A.g−1. Additionally, the device displayed impressive energy and power densities, reaching 31.1 Wh.kg−1 and 14040 W.kg−1, respectively. Moreover, the BWSq SSC device demonstrated notable cyclic stability, manifesting a capacity retention of 62% over 5000 galvanostatic charge-discharge cycles. The outcomes of this study suggest that the BWSq nanostructure holds immense promise as a prospective contender for energy storage applications, offering great potential for practical implementation. • A novel SnO 2 quantum dots interspersed Bi 2 WO 6 nanoflowers (BWSq) electrode material prepared for supercapacitor. • BWSq demonstrates superior specific capacitance, rate capability, and cycling stability compared to Bi 2 WO 6 nanoflowers (BW). • Fabrication and evaluation of a high-performance symmetric supercapacitor (SSC) using BWSq electrodes. • Enhanced charge transfer behavior in BWSq electrodes, highlighting their potential for advanced energy storage applications. [ABSTRACT FROM AUTHOR]