Design of a novel intelligent computing framework for predictive solutions of malaria propagation model.

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.

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator.

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.

Multiclass classification of diseased grape leaf identification using deep convolutional neural network(DCNN) classifier.

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.

Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women.

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.

Analysis and dynamical structure of glucose insulin glucagon system with Mittage-Leffler kernel for type I diabetes mellitus.

In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel. Results are derived for normal and type 1 diabetes at different initial conditions, which support the theoretical observations. These results play an important role in the glucose-insulin-glucagon system in the sense of a closed-loop design, which is helpful for the development of artificial pancreas to control diabetes in society.

Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas.

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.

A framework for the analysis of skin sores disease using evolutionary intelligent computing approach.

The most common and contagious bacterial skin disease i.e. skin sores (impetigo) mostly affects newborns and young children. On the face, particularly around the mouth and nose area, as well as on the hands and feet, it typically manifests as reddish sores. In this study, a neuro-evolutionary global algorithm is introduced to solve the dynamics of nonlinear skin sores disease model (SSDM) with the help of an artificial neural network. The global genetic algorithm is integrated with local sequential quadratic programming (GA-LSQP) to obtain the optimal solution for the proposed model. The designed differential model of skin sores disease is comprised of susceptible (S), infected (I), and recovered (R) categories. An activation function based neural network modeling is exploited for skin sores system through mean square error to achieve best trained weights. The integrated approach is validated and verified through the comparison of results of reference Adam strategy with absolute error analysis. The absolute error results give accuracy of around 10-11 to 10-5, demonstrating the worthiness and efficacy of proposed algorithm. Additionally, statistical investigations in form of mean absolute deviation, root mean square error, and Theil's inequality coefficient are exhibited to prove the consistency, stability, and convergence criteria of the integrated technique. The accuracy of the proposed solver has been examined from the smaller values of minimum, median, maximum, mean, semi-interquartile range, and standard deviation, which lie around 10-12 to 10-2.

Optimal and total controllability approach of non-instantaneous Hilfer fractional derivative with integral boundary condition.

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.

Designing a novel fractional order mathematical model for COVID-19 incorporating lockdown measures.

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 [Formula: see text], infected [Formula: see text], treated [Formula: see text], and recovered [Formula: see text] with the susceptible category further divided into two subcategories [Formula: see text] and [Formula: see text]. 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.

Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator.

Respiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.

Cattaneo-Christov heat flow model at mixed impulse stagnation point past a Riga plate: Levenberg-Marquardt backpropagation method.

Applications of artificial intelligence (AI) via soft computing procedures have attracted the attention of researchers due to their effective modeling, simulation procedures, and detailed analysis. In this article, the designing of intelligence computing through a neural network that is backpropagated with the Levenberg-Marquardt method (NN-BLMM) to study the Cattaneo-Christov heat flow model at the mixed impulse stagnation point (CCHFM-MISP) past a Riga plate is investigated. The original model CCHFM-MISP in terms of PDEs is converted into non-linear ODEs through suitable similarity variables. A data set is generated for all scenarios of CCHFM-MISP through Lobatto IIIA numerical solver by varying Hartman number, velocity ratio parameter, inverse Darcy number, mixed impulse variable, non-dimensional constraint, Eckert number, heat generation variable, Prandtl number, thermal relaxation variable. To find the physical impacts of parameters of interest associated with the presented fluidic system CCHFM-MISP, the approximate solution of NN-BLMM is carried out by performing training (80 %), testing (10 %), and validation (10 %), and then the results are equated with the reference data to ensure the perfection of the proposed model. Through MSE, state transition, error histogram, and regression analysis, the outcomes of NN-BLMM are presented and analyzed. The graphical illustration and numerical outcomes confirm the authentication and effectiveness of the solver. Moreover, mean square errors for validation, training and testing data points along with performance measures lie around 10-10 and the solution plots generated through deterministic (Lobatto IIIA) approach and stochastic numerical solver are matching up to 10-6, which surely validate the solver NN-BLMM. The outcomes of M and B on velocity present the similar impacts. The velocity of material particles decreases under Da while, it increases through velocity ratio and magnetic parameters.

Generalized Ulam-Hyers-Rassias stability and novel sustainable techniques for dynamical analysis of global warming impact on ecosystem.

Marine structure changes as a result of climate change, with potential biological implications for human societies and marine ecosystems. These changes include changes in temperatures, flow, discrimination, nutritional inputs, oxygen availability, and acidification of the ocean. In this study, a fractional-order model is constructed using the Caputo fractional operator, which singular and nol-local kernel. A model examines the effects of accelerating global warming on aquatic ecosystems while taking into account variables that change over time, such as the environment and organisms. The positively invariant area also demonstrates positive, bounded solutions of the model treated. The equilibrium states for the occurrence and extinction of fish populations are derived for a feasible solution of the system. We also used fixed-point theorems to analyze the existence and uniqueness of the model. The generalized Ulam-Hyers-Rassias function is used to analyze the stability of the system. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the power law kernel and also compared the results with an exponential law and Mittag Leffler kernel. We also produce graphs of the model at various fractional derivative orders to illustrate the important influence that the fractional order has on the different classes of the model with the memory effects of the fractional operator. To help with the oversight of fisheries, this research builds mathematical connections between the natural world and aquatic ecosystems.

Intelligent computing for MHD radiative Von Kármán Casson nanofluid along Darcy-Fochheimer medium with activation energy.

The impact of activation energy in chemical processes, heat radiations, and temperature gradients on non-Darcian steady MHD convective Casson nanofluid flows (NMHD-CCNF) over a radial elongated circular cylinder is investigated in this study. The network of partial differential equations (PDEs) for NMHD-CCNF is developed using the modified Buongiorno framework, and the network of controlling PDEs is then transformed into ordinary differential equations (ODEs) utilizing the Von Karman method. Finally, the resulting non-linear ODEs are computed using the ND-solve approach to produce sets of data to assess the proposed model's skills, which can then be handled using the Bayesian Regularization technique of artificial neural networks (BRT-ANN). A novel stochastic computing-based application is being developed to evaluate the importance of NMHD-CCNF across a spinning disc that is radially stretched. The novelty and significance of results for better understanding, clarity, and highlighting the innovative contributions and significance of the proposed scheme. Further, to check the validity of the defined results for NMHD-CCNF, error charts, validation, and mean squared error suggestions are employed. The impact of multiple physical parameters on concentration, radial and tangential velocities, and temperature profiles is shown via tables and figures. Additionally, the results demonstrate that as the Forchheimer number, Casson nanofluid parameter, magnetic parameter, and porosity parameter are strengthened, the radial and rotational nanofluid mobility drops dramatically. The stretching parameter, on the other hand, has a parallel developmental trend. The heat generation parameter, the thermophoresis process, the thermal radiation parameter, and the Brownian motion of nanoparticles can all be increased to give thermal enhancement. On the other side, with larger estimates in thermophoresis parameters and the activation energy, there is a noticeable increase in the concentration profile.

Compatible extension of the (G'/G)-expansion approach for equations with conformable derivative.

In this study, the compatible extensions of the (G'/G)-expansion approach and the generalized (G'/G)-expansion scheme are proposed to generate scores of radical closed-form solutions of nonlinear fractional evolution equations. The originality and improvements of the extensions are confirmed by their application to the fractional space-time paired Burgers equations. The application of the proposed extensions highlights their effectiveness by providing dissimilar solutions for assorted physical forms in nonlinear science. In order to explain some of the wave solutions geometrically, we represent them as two- and three-dimensional graphs. The results demonstrate that the techniques presented in this study are effective and straightforward ways to address a variety of equations in mathematical physics with conformable derivative.

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium.

This article aims to investigate the analytical nature and approximate solution of the radiated flow of electrically conductive viscous fluid into a porous medium with slip effects (RFECVF). In order to build acceptable accurate solutions for RFECVF, this study presented an efficient Levenberg-Marquardt technique of artificial neural networks (LMT-ANNs) approach. One of its fastest back-propagation algorithms for nonlinear lowest latency is the LMT. To turn a quasi-network of PDEs expressing RFECVF into a set of standards, the appropriate adjustments are required. During the flow, the boundary is assumed to be convective. The flow and heat transfer are governed by partial differential equations, and similarity transform is the main tool to convert it into a coupled nonlinear system of ODEs. The usefulness of the constructed LMT-ANNs for such a modelled issue is demonstrated by the best promising algebraic outputs in the E-03 to E-08 range, as well as error histogram and regression analysis measures. Mu is a controller that oversees the entire training procedure. The LMT-ANNs mainly focuses on the higher accuracy of nonlinear systems. Analytical results for the improved boundary layer ODEs are produced using the Variational Iteration Method, a tried-and-true method (VIM). The Lagrange Multiplier is a powerful tool in the suggested method for reducing the amount of computing required. Further, a tabular comparison is provided to demonstrate the usefulness of this study. The final results of the Variational Iteration Method (VIM) in MATLAB have accurately depicted the physical characteristics of a number of parameters, including Eckert, Prandtl, Magnetic, and Thermal radiation parameters.

A design of neuro-computational approach for double-diffusive natural convection nanofluid flow.

The artificial intelligence based neural networking with Back Propagated Levenberg-Marquardt method (NN-BPLMM) is developed to explore the modeling of double-diffusive free convection nanofluid flow considering suction/injection, Brownian motion and thermophoresis effects past an inclined permeable sheet implanted in a porous medium. By applying suitable transformations, the PDEs presenting the proposed problem are transformed into ordinary ones. A reference dataset of NN-BPLMM is fabricated for multiple influential variants of the model representing scenarios by applying Lobatto III-A numerical technique. The reference data is trained through testing, training and validation operations to optimize and compare the approximated solution with desired (standard) results. The reliability, steadiness, capability and robustness of NN-BPLMM is authenticated through MSE based fitness curves, error through histograms, regression illustrations and absolute errors. The investigations suggest that the temperature enhances with the upsurge in thermophoresis impact during suction and decays for injection, whereas increasing Brownian effect decreases the temperature in the presence of wall suction and reverse behavior is seen for injection. The best measures of performance in form of mean square errors are attained as 7.1058 × 10 - 10 , 2.9262 × 10 - 10 , 1.1652 × 10 - 08 , 1.5657 × 10 - 10 and 5.5652 × 10 - 10 against 969, 824, 467, 277 and 650 iterations. The comparative study signifies the authenticity of proposed solver with the absolute errors about 10-7 to 10-3 for all influential parameters results.

Dynamics of two-step reversible enzymatic reaction under fractional derivative with Mittag-Leffler Kernel.

Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it.

A mathematical model for the co-dynamics of COVID-19 and tuberculosis.

In this study, we formulated and analyzed a deterministic mathematical model for the co-infection of COVID-19 and tuberculosis, to study the co-dynamics and impact of each disease in a given population. Using each disease's corresponding reproduction number, the existence and stability of the disease-free equilibrium were established. When the respective threshold quantities R C , and R T are below unity, the COVID-19 and TB-free equilibrium are said to be locally asymptotically stable. The impact of vaccine (i.e., efficacy and vaccinated proportion) and the condition required for COVID-19 eradication was examined. Furthermore, the presence of the endemic equilibria of the sub-models is analyzed and the criteria for the phenomenon of backward bifurcation of the COVID-19 sub-model are presented. To better understand how each disease condition impacts the dynamics behavior of the other, we investigate the invasion criterion of each disease by computing the threshold quantity known as the invasion reproduction number. We perform a numerical simulation to investigate the impact of threshold quantities ( R C , R T ) with respect to their invasion reproduction number, co-infection transmission rate ( ß c t ) , and each disease transmission rate ( ß c , ß t ) on disease dynamics. The outcomes established the necessity for the coexistence or elimination of both diseases from the communities. Overall, our findings imply that while COVID-19 incidence decreases with co-infection prevalence, the burden of tuberculosis on the human population increases.