Numerical Simulation and Design of COVID-19 Forecasting Framework Using Efficient Data Analytics Methodologies

The COVID-19 pandemic hit globally in December 2019 when a certain virus strain from Wuhan, China started proliferating throughout the world. By the end of March 2020, lockdowns and curfews were imposed all over the world halting trade, commerce, education, and various other essential activities. It has been nearly a year since the WHO declared a pandemic but there is still a consistent rise of the cases even with the administration of various types of vaccines and preventive measure. One of the main struggles that the healthcare workers face is to find out the how the virus is spreading amongst a community. The knowledge of this can be used to stop the spread of virus. This is a very important step towards getting things back into momentum to restore activities globally. Many attempts have been made under epidemiology to study the spread of COVID and many mathematical models have emerged as a result that can help with this. A popular model that is used for estimating the effective reproduction number (Rt) has the shortcoming that it cannot simultaneously forecast the future number of cases. This work explores an extension of another model, the SIR-model, in which the model parameters are fitted to recorded data. This makes the model adaptive, opening up the possibilities for estimating the Rt daily and making predictions of future number of confirmed cases. The paper use this adaptive SIR-model (aSIR) to estimate the Rt and create forecasts of new cases in India. The paper purpose is to determine how precise aSIR-models are at estimating the Rt (when compared with FHM’s model). It will also analyze how accurate aSIR-models are at simultaneously forecasting the future spread of Covid-19 in India. The coronavirus spread can be mathematically modelled using factors such as the number of susceptible people, exposed people, infected people, asymptotic people and the number of recovered people. The Khan-Atangana system is an integer-order coronavirus model that uses the above-mentioned factors. Since the coronavirus model depends on the initial conditions, the Khan-Atangana model uses the Atangana-Baleanu operate as it has a non-variant and non-local kernel. Instead, we replace the equations with fractional-order derivatives using the Grünwald-Letnikov derivative. The fractional order derivatives need to be fed with initial conditions and are useful to determine the spread due to their non-local nature. This project proposes to solve these fractional-order derivatives using numerical methods and analyse the stability of this epidemiological model

A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model

A computer network can detect potential viruses through the use of kill signals, thereby minimizing the risk of virus propagation. In the realm of computer security and defensive strategies, computer viruses play a significant role. Understanding of their spread and extension is a crucial component. To address this issue of computer virus spread, we employ a fractional epidemiological SIRA model by utilizing the Caputo derivative. To solve the fractional-order computer virus model, we employ a computational technique known as the Jacobi collocation operational matrix method. This operational matrix transforms the problem of arbitrary order into a system of nonlinear algebraic equations. To analyze this system of arbitrary order, we derive an approximate solution for the fractional computer virus model, also considering the Vieta Lucas polynomials. Numerical simulations are performed and graphical representations are provided to illustrate the impact of order of the fractional derivative on different profiles

Neural networking study of worms in a wireless sensor model in the sense of fractal fractional

We are concerned with the analysis of the neural networks of worms in wireless sensor networks (WSN). The concerned process is considered in the form of a mathematical system in the context of fractal fractional differential operators. In addition, the Banach contraction technique is utilized to achieve the existence and unique outcomes of the given model. Further, the stability of the proposed model is analyzed through functional analysis and the Ulam-Hyers (UH) stability technique. In the last, a numerical scheme is established to check the dynamical behavior of the fractional fractal order WSN model

X-ware: a proof of concept malware utilizing artificial intelligence

Recent years have witnessed a dramatic growth in utilizing computational intelligence techniques for various domains. Coherently, malicious actors are expected to utilize these techniques against current security solutions. Despite the importance of these new potential threats, there remains a paucity of evidence on leveraging these research literature techniques. This article investigates the possibility of combining artificial neural networks and swarm intelligence to generate a new type of malware. We successfully created a proof of concept malware named X-ware, which we tested against the Windows-based systems. Developing this proof of concept may allow us to identify this potential threat’s characteristics for developing mitigation methods in the future. Furthermore, a method for recording the virus’s behavior and propagation throughout a file system is presented. The proposed virus prototype acts as a swarm system with a neural network-integrated for operations. The virus’s behavioral data is recorded and shown under a complex network format to describe the behavior and communication of the swarm. This paper has demonstrated that malware strengthened with computational intelligence is a credible threat. We envisage that our study can be utilized to assist current and future security researchers to help in implementing more effective countermeasure

A New Efficient Technique for Solving Modified Chua's Circuit Model with a New Fractional Operator

Chua's circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua's circuit is obtained by transforming the classical model of Chua's circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua's circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations are given to show the applicability of the algorithms, and effective graphics are sketched for comparison purposes of the newly introduced fractional operatorsThe authors are grateful to the Spanish Government for Grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE) and to the Basque Government for Grant IT1207-1

Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation

In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches. Many graphical representations such as 2D, 3D and contour are also reported. Finally, general conclusions of about the novel findings are introduced at the end of this manuscript

A novel design of fractional Mayer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems

In this study, a novel stochastic computational frameworks based on fractional Meyer wavelet artificial neural network (FMW-ANN) is designed for nonlinear-singular fractional Lane-Emden (NS-FLE) differential equation. The modeling strength of FMW-ANN is used to transformed the differential NS-FLE system to difference equations and approximate theory is implemented in mean squared error sense to develop a merit function for NS-FLE differential equations. Meta-heuristic strength of hybrid computing by exploiting global search efficacy of genetic algorithms (GA) supported with local refinements with efficient active-set (AS) algorithm is used for optimization of design variables FMW-ANN., i.e., FMW-ANN-GASA. The proposed FMW-ANN-GASA methodology is implemented on NS-FLM for six different scenarios in order to exam the accuracy, convergence, stability and robustness. The proposed numerical results of FMW-ANN-GASA are compared with exact solutions to verify the correctness, viability and efficacy. The statistical observations further validate the worth of FMW-ANN-GASA for the solution of singular nonlinear fractional order systems.This paper is partially supported by Ministerio de Ciencia, Innovación y Universidades grant number PGC2018-097198-BI00 and Fundación Séneca de la Región de Murcia grant number 20783/PI/18

NUMERICAL AND THEORETICAL INVESTIGATIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS

Fractional calculus has been recently received huge attention from Mathematicians and engineers due to its importance in many real-life applications such as: fluid mechanics, electromagnetic, acoustics, chemistry, biology, physics and material sciences. In this thesis, we present numerical algorithms for solving fractional IVPs and system of fractional IVPs where two types of fractional derivatives are used: Caputo-Fabrizio, and Atangana-Baleanu-Caputo derivatives. These algorithms are developed based on modified Adams-Bashforth method. In addition, we discuss the theoretical solution of special class of fractional IVPs. Several examples are discussed to illustrate the efficiency and accuracy of the present schemes

Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms

The objective of this article is to present the computable solution of space-time advection-dispersion equation of fractional order associated with Hilfer-Prabhakar fractional derivative operator as well as fractional Laplace operator. The method followed in deriving the solution is that of joint Sumudu and Fourier transforms. The solution is derived in compact and graceful forms in terms of the generalized Mittag-Leffler function, which is suitable for numerical computation. Some illustration and special cases of main theorem are also discussed

Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications

We investigate the probabilistic and analytic properties of Volterra processes constructed as pathwise integrals of deterministic kernels with respect to the H\"older continuous trajectories of Hilbert-valued Gaussian processes. To this end, we extend the Volterra sewing lemma from \cite{HarangTindel} to the two dimensional case, in order to construct two dimensional operator-valued Volterra integrals of Young type. We prove that the covariance operator associated to infinite dimensional Volterra processes can be represented by such a two dimensional integral, which extends the current notion of representation for such covariance operators. We then discuss a series of applications of these results, including the construction of a rough path associated to a Volterra process driven by Gaussian noise with possibly irregular covariance structures, as well as a description of the irregular covariance structure arising from Gaussian processes time-shifted along irregular trajectories. Furthermore, we consider an infinite dimensional fractional Ornstein-Uhlenbeck process driven by Gaussian noise, which can be seen as an extension of the volatility model proposed by Rosenbaum et al. in \cite{ElEuchRosenbaum}.Comment: 38 page