A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network

The purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission model(FDTM)in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network(LM-NN)technique.The fractional dengue transmission model(FDTM)consists of 12 compartments.The human population is divided into four compartments;susceptible humans(S_(h)),exposed humans(E_(h)),infectious humans(I_(h)),and recovered humans(R_(h)).Wolbachia-infected and Wolbachia-uninfected mosquito population is also divided into four compartments:aquatic(eggs,larvae,pupae),susceptible,exposed,and infectious.We investigated three different cases of vertical transmission probability(η),namely when Wolbachia-free mosquitoes persist only(η=0.6),when both types of mosquitoes persist(η=0.8),and when Wolbachia-carrying mosquitoes persist only(η=1).The objective of this study is to investigate the effectiveness of Wolbachia in reducing dengue and presenting the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three different cases of the fractional order derivatives(α=0.4,0.6,0.8).LM-NN approach includes a training,validation,and testing procedure to minimize the mean square error(MSE)values using the reference dataset(obtained by solving the model using the Adams-Bashforth-Moulton method(ABM).The distribution of data is 80% data for training,10% for validation,and,10% for testing purpose)results.A comprehensive investigation is accessible to observe the competence,precision,capacity,and efficiency of the suggested LM-NN approach by executing the MSE,state transitions findings,and regression analysis.The effectiveness of the LM-NN approach for solving the FDTM is demonstrated by the overlap of the findings with trustworthy measures,which achieves a precision of up to 10^(-4).

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.

A novel fractional case study of nonlinear dynamics via analytical approach

The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.

Stochastic Analysis for the Dynamics of a Poliovirus Epidemic Model

Most developing countries such as Afghanistan,Pakistan,India,Bangladesh,and many more are still fighting against poliovirus.According to the World Health Organization,approximately eighteen million people have been infected with poliovirus in the last two decades.In Asia,still,some countries are suffering from the virus.The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied.Some basic properties of the deterministic model are studied,equilibria,local stability around the stead states,and reproduction number.Euler Maruyama,stochastic Euler,and stochastic Runge-Kutta study the behavior of complex stochastic differential equations.The main target of this study is to develop a nonstandard computational method that restores dynamical features like positivity,boundedness,and dynamical consistency.Unfortunately,the existing methods failed to fix the actual behavior of the disease.The comparison of the proposed approach with existing methods is investigated.

A Study on the Nonlinear Caputo-Type Snakebite Envenoming Model with Memory

In this article,we introduce a nonlinear Caputo-type snakebite envenoming model with memory.The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractionalorder sense.The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector(L1-PC)scheme with error estimation and stability analysis.The proof of the existence and positivity of the solution is given by using the fixed point theory.From the necessary simulations,we justify that the first-time implementation of the proposedmethod on an epidemicmodel shows that the scheme is fully suitable and time-efficient for solving epidemic models.This work aims to show the novel application of the given scheme as well as to check how the proposed snakebite envenoming model behaves in the presence of the Caputo fractional derivative,including memory effects.

Image Splicing Detection Using Generalized Whittaker Function Descriptor

Image forgery is a crucial part of the transmission of misinformation,which may be illegal in some jurisdictions.The powerful image editing software has made it nearly impossible to detect altered images with the naked eye.Images must be protected against attempts to manipulate them.Image authentication methods have gained popularity because of their use in multimedia and multimedia networking applications.Attempts were made to address the consequences of image forgeries by creating algorithms for identifying altered images.Because image tampering detection targets processing techniques such as object removal or addition,identifying altered images remains a major challenge in research.In this study,a novel image texture feature extraction model based on the generalized k-symbolWhittaker function(GKSWF)is proposed for better image forgery detection.The proposed method is divided into two stages.The first stage involves feature extraction using the proposed GKSWF model,followed by classification using the“support vector machine”(SVM)to distinguish between authentic and manipulated images.Each extracted feature from an input image is saved in the features database for use in image splicing detection.The proposed GKSWF as a feature extraction model is intended to extract clues of tampering texture details based on the probability of image pixel.When tested on publicly available image dataset“CASIA”v2.0(ChineseAcademy of Sciences,Institute of Automation),the proposed model had a 98.60%accuracy rate on the YCbCr(luminance(Y),chroma blue(Cb)and chroma red(Cr))color spaces in image block size of 8×8 pixels.The proposed image authentication model shows great accuracy with a relatively modest dimension feature size,supporting the benefit of utilizing the k-symbol Whittaker function in image authentication algorithms.

Pixel’s Quantum Image Enhancement Using Quantum Calculus

The current study provides a quantum calculus-based medical image enhancement technique that dynamically chooses the spatial distribution of image pixel intensity values.The technique focuses on boosting the edges and texture of an image while leaving the smooth areas alone.The brain Magnetic Resonance Imaging(MRI)scans are used to visualize the tumors that have spread throughout the brain in order to gain a better understanding of the stage of brain cancer.Accurately detecting brain cancer is a complex challenge that the medical system faces when diagnosing the disease.To solve this issue,this research offers a quantum calculus-based MRI image enhancement as a pre-processing step for brain cancer diagnosis.The proposed image enhancement approach improves images with low gray level changes by estimating the pixel’s quantum probability.The suggested image enhancement technique is demonstrated to be robust and resistant to major quality changes on a variety ofMRIscan datasets of variable quality.ForMRI scans,the BRISQUE“blind/referenceless image spatial quality evaluator”and the NIQE“natural image quality evaluator”measures were 39.38 and 3.58,respectively.The proposed image enhancement model,according to the data,produces the best image quality ratings,and it may be able to aid medical experts in the diagnosis process.The experimental results were achieved using a publicly available collection of MRI scans.

Stability Scrutinization of Agrawal Axisymmetric Flow of Nanofluid through a Permeable Moving Disk Due to Renewable Solar Radiation with Smoluchowski Temperature and Maxwell Velocity Slip Boundary Conditions

The utilization of solar energy is essential to all living things since the beginning of time.In addition to being a constant source of energy,solar energy(SE)can also be used to generate heat and electricity.Recent technology enables to convert the solar energy into electricity by using thermal solar heat.Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy.Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly.The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy.Moreover,the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer.The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically.The current numerical approach can produce double solutions by providing suitable initial guesses.In addition,the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction.The suction parameter delays the boundary layer separation.Moreover,stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable.

AWeighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

In the present paper,the numerical solution of It?type stochastic parabolic equation with a timewhite noise process is imparted based on a stochastic finite difference scheme.At the beginning,an implicit stochastic finite difference scheme is presented for this equation.Some mathematical analyses of the scheme are then discussed.Lastly,to ascertain the efficacy and accuracy of the suggested technique,the numerical results are discussed and compared with the exact solution.

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

The first major outbreak of the severely complicated hand,foot and mouth disease(HFMD),primarily caused by enterovirus 71,was reported in Taiwan in 1998.HFMD surveillance is needed to assess the spread of HFMD.The parameters we use in mathematical models are usually classical mathematical parameters,called crisp parameters,which are taken for granted.But any biological or physical phenomenon is best explained by uncertainty.To represent a realistic situation in any mathematical model,fuzzy parameters can be very useful.Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling.However,few works use fuzzy theory in building models to simulateHFMDdynamics.In this context,we examined anHFMD model with fuzzy parameters.A Non Standard Finite Difference(NSFD)scheme is developed to solve the model.The developed technique retains essential properties such as positivity and dynamic consistency.Numerical simulations are presented to support the analytical results.The convergence and consistency of the proposed method are also discussed.The proposed method converges unconditionally while the many classical methods in the literature do not possess this property.In this regard,our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

Modeling of Computer Virus Propagation with Fuzzy Parameters

Typically,a computer has infectivity as soon as it is infected.It is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the Internet.To understand the dynamics of the virus propagation in a better way,a computer virus spread model with fuzzy parameters is presented in this work.It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity,which depends on the quantity of virus.Considering this,the parametersβandγbeing functions of the computer virus load,are considered fuzzy numbers.Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models.The essential features of the model,like reproduction number and equilibrium analysis,are discussed in fuzzy senses.Moreover,with fuzziness,two numerical methods,the forward Euler technique,and a nonstandard finite difference(NSFD)scheme,respectively,are developed and analyzed.In the evidence of the numerical simulations,the proposed NSFD method preserves the main features of the dynamic system.It can be considered a reliable tool to predict such types of solutions.

Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment

The application of fuzzy theory is vital in all scientific disciplines.The construction of mathematical models with fuzziness is little studied in the literature.With this in mind and for a better understanding of the disease,an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classicalmodel ofmalaria transmission.The parametersβandδ,being function of the malaria virus load,are considered fuzzy numbers.Three steady states and the reproduction number of the model are analyzed in fuzzy senses.A numerical technique is developed in a fuzzy environment to solve the studied model,which retains essential properties such as positivity and dynamic consistency.Moreover,numerical simulations are carried out to illustrate the analytical results of the developed technique.Unlike most of the classical methods in the literature,the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.

Computational Analysis for Computer Network Model with Fuzziness

A susceptible,exposed,infectious,quarantined and recovered(SEIQR)model with fuzzy parameters is studied in this work.Fuzziness in the model arises due to the different degrees of susceptibility,exposure,infectivity,quarantine and recovery among the computers under consideration due to the different sizes,models,spare parts,the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus,etc.Each individual PC has a different degree of infectivity and resis-tance against infection.In this scenario,the fuzzy model has richer dynamics than its classical counterpart in epidemiology.The reproduction number of the developed model is studied and the equilibrium analysis is performed.Two different techniques are employed to solve the model numerically.Numerical simulations are performed and the obtained results are compared.Positivity and convergence are maintained by the suggested technique which are the main features of the epidemic models.

Introduction to the Special Issue on Mathematical Aspects of Computational Biology and Bioinformatics

The special issue presents new mathematical and computational approaches,to investigate some core problems of the computational biological sciences.This topic presents a huge interest from both theoretical and applied viewpoints.The content of this special issue was focused mainly to debate a wide range of the theory and applications of integer-order and fractional-order derivatives and fractional-order integrals in different directions of mathematical biology.Several interdisciplinary groups reported their related results.

Optimization of Coronavirus Pandemic Model Through Artificial Intelligence

Artificial intelligence is demonstrated by machines,unlike the natural intelligence displayed by animals,including humans.Artificial intelligence research has been defined as the field of study of intelligent agents,which refers to any system that perceives its environment and takes actions that maximize its chance of achieving its goals.The techniques of intelligent computing solve many applications of mathematical modeling.The researchworkwas designed via a particularmethod of artificial neural networks to solve the mathematical model of coronavirus.The representation of the mathematical model is made via systems of nonlinear ordinary differential equations.These differential equations are established by collecting the susceptible,the exposed,the symptomatic,super spreaders,infection with asymptomatic,hospitalized,recovery,and fatality classes.The generation of the coronavirus model’s dataset is exploited by the strength of the explicit Runge Kutta method for different countries like India,Pakistan,Italy,and many more.The generated dataset is approximately used for training,validation,and testing processes for each cyclic update in Bayesian Regularization Backpropagation for the numerical treatment of the dynamics of the desired model.The performance and effectiveness of the designed methodology are checked through mean squared error,error histograms,numerical solutions,absolute error,and regression analysis.

Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics

The human immunodeficiency viruses are two species of Lentivirus that infect humans.Over time,they cause acquired immunodeficiency syndrome,a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive.Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa.Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s.Over decades,human immunodeficiency viruses slowly spread across Africa and later into other parts of the world.The Susceptible-Infected-Recovered(SIR)models are significant in studying disease dynamics.In this paper,we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods.Euler,Runge Kutta,and a Non-standardfinite difference(NSFD)method are developed for the same problem.Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes‘ℎ’.The results reveal that,unlike Euler and Runge Kutta,which fail for large time step sizes,the proposed Non-standardfinite difference(NSFD)method gives a convergence solution for any time step size.Our proposed numerical method is bounded,dynamically con-sistent,and preserves the positivity of the continuous solution,which are essential requirements when modeling a prevalent disease.

Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model

Mathematical delay modelling has a significant role in the different disciplines such as behavioural,social,physical,biological engineering,and bio-mathematical sciences.The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus(COVID-19).Due to the unavailability of vaccines for the coronavirus worldwide,delay factors such as social distance,quarantine,travel restrictions,extended holidays,hospitalization,and isolation have contributed to controlling the coronavirus epidemic.We have analysed the reproduction number and its sensitivity to parameters.If,R_(covid)>1then this situation will help to eradicate the disease and if,R_(covid)>1 the virus will spread rapidly in the human beings.Well-known theorems such as Routh Hurwitz criteria and Lasalle invariance principle have presented for stability.The local and global stabilizes for both equilibria of the model have also been presented.Also,we have analysed the effect of delay reason on the reproduction number.In the last,some very useful numerical consequences have presented in support of hypothetical analysis.

Planar System-Masses in an Equilateral Triangle:Numerical Study within Fractional Calculus

In this work,a system of three masses on the vertices of equilateral triangle is investigated.This system is known in the literature as a planar system.We first give a description to the system by constructing its classical Lagrangian.Secondly,the classical Euler-Lagrange equations(i.e.,the classical equations of motion)are derived.Thirdly,we fractionalize the classical Lagrangian of the system,and as a result,we obtain the fractional Euler-Lagrange equations.As the final step,we give the numerical simulations of the fractional model,a new model which is based on Caputo fractional derivative.

A New Medical Image Enhancement Algorithm Based on Fractional Calculus

The enhancement of medical images is a challenging research task due to the unforeseeable variation in the quality of the captured images.The captured images may present with low contrast and low visibility,which might inuence the accuracy of the diagnosis process.To overcome this problem,this paper presents a new fractional integral entropy(FITE)that estimates the unforeseeable probabilities of image pixels,posing as the main contribution of the paper.The proposed model dynamically enhances the image based on the image contents.The main advantage of FITE lies in its capability to enhance the low contrast intensities through pixels’probability.Initially,the pixel probability of the fractional power is utilized to extract the illumination value from the pixels of the image.Next,the contrast of the image is then adjusted to enhance the regions with low visibility.Finally,the fractional integral entropy approach is implemented to enhance the low visibility contents from the input image.Tests were conducted on brain MRI,lungs CT,and kidney MRI scans datasets of different image qualities to show that the proposed model is robust and can withstand dramatic variations in quality.The obtained comparative results show that the proposed image enhancement model achieves the best BRISQUE and NIQE scores.Overall,this model improves the details of brain MRI,lungs CT,and kidney MRI scans,and could therefore potentially help the medical staff during the diagnosis process.