The aim of this work is to design an intelligent computing paradigm through Levenberg-Marquardt artificial neural networks (LMANNs) for solving the mathematical model of Corona virus disease 19 (COVID-19) propagation via human to human interaction. The model is represented with systems of nonlinear ordinary differential equations represented with susceptible, exposed, symptomatic and infectious, super spreaders, infection but asymptomatic, hospitalized, recovery and fatality classes, and reference dataset of the COVID-19 model is generated by exploiting the strength of explicit Runge-Kutta numerical method for metropolitans of China and Pakistan including Wuhan, Karachi, Lahore, Rawalpindi and Faisalabad. The created dataset is arbitrary used for training, validation and testing processes for each cyclic update in Levenberg-Marquardt backpropagation for numerical treatment of the dynamics of COVID-19 model. The effectiveness and reliable performance of the design LMANNs are endorsed on the basis of assessments of achieved accuracy in terms of mean squared error based merit functions, error histograms and regression studies.
The objective of the current investigation is to examine the influence of variable viscosity and transverse magnetic field on mixed convection fluid model through stretching sheet based on copper and silver nanoparticles by exploiting the strength of numerical computing via Lobatto IIIA solver. The nonlinear partial differential equations are changed into ordinary differential equations by means of similarity transformations procedure. A renewed finite difference based Lobatto IIIA method is incorporated to solve the fluidic system numerically. Vogel's model is considered to observe the influence of variable viscosity and applied oblique magnetic field with mixed convection along with temperature dependent viscosity. Graphical and numerical illustrations are presented to visualize the behavior of different sundry parameters of interest on velocity and temperature. Outcomes reflect that volumetric fraction of nanoparticles causes to increase the thermal conductivity of the fluid and the temperature enhances due to blade type copper nanoparticles. The convergence analysis on the accuracy to solve the problem is investigated viably though the residual errors with different tolerances to prove the worth of the solver. The temperature of the fluid accelerates due the blade type nanoparticles of copper and skin friction coefficient is reduced due to enhancement of Grashof Number.
A novel numerical computing framework through Lobatto IIIA method is presented for the dynamical investigation of nanofluidic problem with Williamson fluid flow on a stretching sheet by considering the thermal slip and velocity. The impact of thermophoresis and brownian motion on phenomena of heat transfer are explored by using Buongiorno model. The governing nonlinear partial differential system representing the mathematical model of the Williamson fluid is transformed in to a system of ODEs by incorporating the competency of non-dimensional similarity variables. The dynamics of the transformed system of ODEs are evaluated through the Lobatto IIIA numerically. Sufficient graphical and numerical illustrations are portrayed in order to investigate and analyze the influence of physical parameters; Williamson parameter, Prandtl number, Lewis number, Schmidt number, ratio of diffusivity parameter and ratio of heat capacitance parameter on velocity, temperature and concentration fields. The numerically computed values of local Nusselt number, local Sherwood number and Skin friction coefficient are also inspected for exhaustive assessment. Moreover, the accuracy, efficiency and stability of the proposed method is analyzed through relative errors.
In this study, a new computing technique is introduced to solve the susceptible-exposed-infected-and-recovery (SEIR) Ebola virus model represented with the system of ordinary differential equations through Levenberg–Marquardt backpropagation neural networks. The dynamics of the SEIR model are examined by the variation in different parameters, such as the increase in the susceptible rate while keeping other parameters fixed, such as the natural death rate of susceptibility, susceptible exposed rate, infected exposed rate, and infected to recovered rate; the four types of infected rates, namely, the natural mortality rate, rate of exposed death due to the disease, natural infected mortality rate, and rate of infected death due to the disease; and the rate of natural mortality of the recovered. The datasets for the SEIR nonlinear system for measuring the effects of Ebola virus disease spread dynamics are generated through the Runge–Kutta method for each scenario. The efficiency of the proposed computing technique—LMBNNs—is analyzed through absolute deviation, mean square error, learning curves, histogram analysis, and regression metrics, which provides a way for validation, testing, and training through the scheme.
In 2020, the reported cases were 0.12 million in the six regions to the official report of the World Health Organization (WHO). For most children infected with leprosy, 0.008629 million cases were detected under fifteen. The total infected ratio of the children population is approximately 4.4 million. Due to the COVID-19 pandemic, the awareness programs implementation has been disturbed. Leprosy disease still has a threat and puts people in danger. Nonlinear delayed modeling is critical in various allied sciences, including computational biology, computational chemistry, computational physics, and computational economics, to name a few. The time delay effect in treating leprosy delayed epidemic model is investigated. The whole population is divided into four groups: those who are susceptible, those who have been exposed, those who have been infected, and those who have been vaccinated. The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven. The parameters' sensitivity is also examined. The analytical analysis is supported by computer results that are presented in a variety of ways. The proposed approach in this paper preserves equilibrium points and their stabilities, the existence and uniqueness of solutions, and the computational ease of implementation.
In 2021, most of the developing countries are fighting polio, and parents are concerned with the disabling of their children. Poliovirus transmits from person to person, which can infect the spinal cord, and paralyzes the parts of the body within a matter of hours. According to the World Health Organization (WHO), 18 million currently healthy people could have been paralyzed by the virus during 1988-2020. Almost all countries but Pakistan, Afghanistan, and a few more have been declared polio-free. The mathematical modeling of poliovirus is studied in the population by categorizing it as susceptible individuals (S), exposed individuals (E), infected individuals (I), and recovered individuals (R). In this study, we study the fundamental properties such as positivity and boundedness of the model. We also rigorously study the model's stability and equilibria with or without poliovirus. For numerical study, we design the Euler, Runge-Kutta, and nonstandard finite difference method. However, the standard techniques are time-dependent and fail to present the results for an extended period. The nonstandard finite difference method works well to study disease dynamics for a long time without any constraints. Finally, the results of different methods are compared to prove their effectiveness.
Artificial intelligence plays a very prominent role in many fields, and of late, this term has been gaining much more popularity due to recent advances in machine learning. Machine learning is a sphere of artificial intelligence where machines are responsible for doing daily chores and are believed to be more intelligent than humans. Furthermore, artificial intelligence is significant in behavioral, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Fractional-order modeling of a real-world problem is a powerful tool for understanding the dynamics of the problem. In this study, an investigation into a fractional-order epidemic model of the novel coronavirus (COVID-19) is presented using intelligent computing through Bayesian-regularization backpropagation networks (BRBFNs). The designed BRBFNs are exploited to predict the transmission dynamics of COVID-19 disease by taking the dataset from a fractional numerical method based on the Grünwald–Letnikov backward finite difference. The datasets for the fractional-order mathematical model of COVID-19 for Wuhan and Karachi metropolitan cities are trained with BRBFNs for biased and unbiased input and target values. The proposed technique (BRBFNs) is implemented to estimate the integer and fractional-order COVID-19 spread dynamics. Its reliability, effectiveness, and validation are verified through consistently achieved accuracy metrics that depend on error histograms, regression studies, and mean squared error.
<abstract><p>A repeatedly infected person is one of the most important barriers to malaria disease eradication in the population. In this article, the effects of recurring malaria re-infection and decline in the spread dynamics of the disease are investigated through a supervised learning based neural networks model for the system of non-linear ordinary differential equations that explains the mathematical form of the malaria disease model which representing malaria disease spread, is divided into two types of systems: Autonomous and non-autonomous, furthermore, it involves the parameters of interest in terms of Susceptible people, Infectious people, Pseudo recovered people, recovered people prone to re-infection, Susceptible mosquito, Infectious mosquito. The purpose of this work is to discuss the dynamics of malaria spread where the problem is solved with the help of Levenberg-Marquardt artificial neural networks (LMANNs). Moreover, the malaria model reference datasets are created by using the strength of the Adams numerical method to utilize the capability and worth of the solver LMANNs for better prediction and analysis. The generated datasets are arbitrarily used in the Levenberg-Marquardt back-propagation for the testing, training, and validation process for the numerical treatment of the malaria model to update each cycle. On the basis of an evaluation of the accuracy achieved in terms of regression analysis, error histograms, mean square error based merit functions, where the reliable performance, convergence and efficacy of design LMANNs is endorsed through fitness plot, auto-correlation and training state.</p></abstract>
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