A besyian regularisation neural network approach for hepatitis B virus spread prediction and immune system therapy model

The primary aim of the article is to analyze the response of the human immune system when it encounters the hepatitis B virus. This is done using a mathematical system of differential equations. The differential equation system has six components, likely representing various aspects of the immune response or virus dynamics. A Bayesian regularization neural network has been presented in the process of training. These networks are employed to find solutions for different categories or scenarios related to hepatitis B infection. The Adams method is used to generate reference data sets. The back-propagated artificial neural network, based on Bayesian regularization, is trained and validated using the generated data. The data is divided into three sets: 90% for training and 5% each for testing and validation. The correctness and effectiveness of the proposed neural network model have been assessed using various evaluation metrics. The metrics have been used in this study are Mean Square Error (MSE), histogram errors, and regression plots. These measures provide support to the neural network to approximate the immune response to the hepatitis B virus.

Intelligent computing framework to analyze the transmission risk of COVID-19: Meyer wavelet artificial neural networks

The optimum control methods for the epidemiology of the COVID-19 model are acknowledged using a novel advanced intelligent computing infrastructure that joins artificial neural networks with unsupervised learning-based optimizers i.e., Genetic Algorithms (GA) and sequential quadratic programming (SQP). Unsupervised learning strategy is provided which depends on the wavelet basis's sequential deconstruction of stochastic data. The weights or selection values of neural networks are utilizing cumulative algorithms of Meyer wavelet artificial neural networks (MWANNs) optimized with global search Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP), referred to as MWANNs-GA-SQP and the design technique is utilized to determine the COVID-19 model for five different scenarios employing different step sizes and input intervals. The findings of this research article examined that in order to minimize the total disease transmission at the lowest cost and complexity, safety, focused medical care, and exterior sterilization methods applicability. The provided data is validated through various graphical simulations, which surely authenticate the effectiveness and robustness of the proposed solver. The suggested solver, MWANNs-GA-SQP, is tested in a variety of circumstances to examine that how reliable, safe, and tolerant. Using the proposed MWANNs hubristic intelligent approach, an objective optimization function is created in feed forward neural networking to minimize the mean square error. An investigation of the hybrid GA-SQP is used to confirm the accuracy and dependability of the MWANNs model results. Mean absolute graphs have been constructed to assess the integrity and efficiency of the proposed methodology. The accuracy and reliability of the suggested method are demonstrated by constantly achieving maximum variables of analytical assessment criteria computed for a large appropriate variety of distinct trials.

A next-generation dynamic programming language Julia: Its features and applications in biological science

BACKGROUND

The advent of Julia as a sophisticated and dynamic programming language in 2012 represented a significant milestone in computational programming, mathematical analysis, and statistical modeling. Having reached its stable release in version 1.9.0 on May 7, 2023, Julia has developed into a powerful and versatile instrument. Despite its potential and widespread adoption across various scientific and technical domains, there exists a noticeable knowledge gap in comprehending its utilization within biological sciences.

THE AIM OF REVIEW

This comprehensive review aims to address this particular knowledge gap and offer a thorough examination of Julia's fundamental characteristics and its applications in biology.

KEY SCIENTIFIC CONCEPTS OF THE REVIEW

The review focuses on a research gap in the biological science. The review aims to equip researchers with knowledge and tools to utilize Julia's capabilities in biological science effectively and to demonstrate the gap. It paves the way for innovative solutions and discoveries in this rapidly evolving field. It encompasses an analysis of Julia's characteristics, packages, and performance compared to the other programming languages in this field. The initial part of this review discusses the key features of Julia, such as its dynamic and interactive nature, fast processing speed, ease of expression manipulation, user-friendly syntax, code readability, strong support for multiple dispatch, and advanced type system. It also explores Julia's capabilities in data analysis, visualization, machine learning, and algorithms, making it suitable for scientific applications. The next section emphasizes the importance of using Julia in biological research, highlighting its seamless integration with biological studies for data analysis, and computational biology. It also compares Julia with other programming languages commonly used in biological research through benchmarking and performance analysis. Additionally, it provides insights into future directions and potential challenges in Julia's applications in biology.

Recurrent neural network for the dynamics of Zika virus spreading

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.

Stochastic intelligent computing solvers for the SIR dynamical prototype epidemic model using the impacts of the hospital bed

The present investigations are related to design a stochastic intelligent solver using the infrastructure of artificial neural networks (ANNs) and scaled conjugate gradient (SCG), i.e. ANNs-SCG for the numerical simulations of SIR dynamical prototype system based impacts of hospital bed. The SIR dynamical model is defined into three classes, susceptible patients in the hospital, infected population and recovered people. The proposed results are obtained through the sample statics of verification, testing and training of the dataset. The selection of the statics for training, testing and validation is chosen as 80%, 8% and 12%. A dataset is proposed based on the Adams scheme for the comparison of dynamical SIR prototype using the impacts of hospital bed. The numerical solutions are presented through the ANNs-SCG in order to reduce the values of the mean square error. To achieve the reliability, capability, accuracy, and competence of ANNs-SCG, the mathematical solutions are presented in the form of error histograms (EHs), regression, state transitions (STs) and correlation.

A neural network computational structure for the fractional order breast cancer model

The current study provides the numerical performances of the fractional kind of breast cancer (FKBC) model, which are based on five different classes including cancer stem cells, healthy cells, tumor cells, excess estrogen, and immune cells. The motive to introduce the fractional order derivatives is to present more precise solutions as compared to integer order. A stochastic computing reliable scheme based on the Levenberg Marquardt backpropagation neural networks (LMBNNS) is proposed to solve three different cases of the fractional order values of the FKBC model. A designed dataset is constructed by using the Adam solver in order to reduce the mean square error by taking the data performances as 9% for both testing and validation, while 82% is used for training. The correctness of the solver is approved through the negligible absolute error and matching of the solutions for each model's case. To validates the accuracy, and consistency of the solver, the performances based on the error histogram, transition state, and regression for solving the FKBC model.

An artificial neural network approach for the language learning model

The current study provides the numerical solutions of the language-based model through the artificial intelligence (AI) procedure based on the scale conjugate gradient neural network (SCJGNN). The mathematical learning language differential model is characterized into three classes, named as unknown, familiar, and mastered. A dataset is generalized by using the performance of the Adam scheme, which is used to reduce to mean square error. The AI based SCJGNN procedure works by taking the data with the ratio of testing (12%), validation (13%), and training (75%). An activation log-sigmoid function, twelve numbers of neurons, SCJG optimization, hidden and output layers are presented in this stochastic computing work for solving the learning language model. The correctness of AI based SCJGNN is noted through the overlapping of the results along with the small calculated absolute error that are around 10-06 to 10-08 for each class of the model. Moreover, the regression performances for each case of the model is performed as one that shows the perfect model. Additionally, the dependability of AI based SCJGNN is approved using the histogram, and function fitness.

Numerical performances through artificial neural networks for solving the vector-borne disease with lifelong immunity

The current study is related to solve a nonlinear vector-borne disease with a lifelong immunity model (VDLIM) by designing a computational stochastic framework using the strength of artificial Levenberg-Marquardt backpropagation neural network (ALMBNN). The detail of the nonlinear VDLIM is provided along with its five classes. The numerical performances of the results have been presented using the ALMBNN by taking three different cases to solve the nonlinear VDLIM using the training, sample data, testing and authentication. The selection of the statics is selected as 80% for training, while the data for both testing and validations is applied 10%. The results of the nonlinear VDLIM are performed using the ALMBNN and the correctness of the scheme is observed to compare the results with the reference solutions. The calculated performance of the results to solve the nonlinear VDLIM is applied for the reduction of the mean square error. In order to check the competence, efficacy, exactness and reliability of the ALMBNN, the numerical investigations using the proportional procedures based on the MSE, correlation, regression and error histograms are presented.

Hybridization of the swarming and interior point algorithms to solve the Rabinovich-Fabrikant system

In this study, a trustworthy swarming computing procedure is demonstrated for solving the nonlinear dynamics of the Rabinovich-Fabrikant system. The nonlinear system's dynamic depends upon the three differential equations. The computational stochastic structure based on the artificial neural networks (ANNs) along with the optimization of global search swarming particle swarm optimization (PSO) and local interior point (IP) algorithms, i.e., ANNs-PSOIP is presented to solve the Rabinovich-Fabrikant system. An objective function based on the differential form of the model is optimized through the local and global search methods. The correctness of the ANNs-PSOIP scheme is observed through the performances of achieved and source solutions, while the negligible absolute error that is around 10^-05-10^-07 also represent the worth of the ANNs-PSOIP algorithm. Furthermore, the consistency of the ANNs-PSOIP scheme is examined by applying different statistical procedures to solve the Rabinovich-Fabrikant system.

Modelling the effects of social distancing, antiviral therapy, and booster shots on mitigating Omicron spread

As the COVID-19 situation changes because of emerging variants and updated vaccines, an elaborate mathematical model is essential in crafting proactive and effective control strategies. We propose a COVID-19 mathematical model considering variants, booster shots, waning, and antiviral drugs. We quantify the effects of social distancing in the Republic of Korea by estimating the reduction in transmission induced by government policies from February 26, 2021 to February 3, 2022. Simulations show that the next epidemic peak can be estimated by investigating the effects of waning immunity. This research emphasizes that booster vaccination should be administered right before the next epidemic wave, which follows the increasing waned population. Policymakers are recommended to monitor the waning population immunity using mathematical models or other predictive methods. Moreover, our simulations considering a new variant's transmissibility, severity, and vaccine evasion suggest intervention measures that can reduce the severity of COVID-19.

A fractional order nonlinear model of the love story of Layla and Majnun

In this study, a fractional order mathematical model using the romantic relations of the Layla and Majnun is numerically simulated by the Levenberg-Marquardt backpropagation neural networks. The fractional order derivatives provide more realistic solutions as compared to integer order derivatives of the mathematical model based on the romantic relationship of the Layla and Majnun. The mathematical formulation of this model has four categories that are based on the system of nonlinear equations. The exactness of the stochastic scheme is observed for solving the romantic mathematical system using the comparison of attained and Adam results. The data for testing, authorization, and training is provided as 15%, 75% and 10%, along with the twelve numbers of hidden neurons. Furthermore, the reducible value of the absolute error improves the accuracy of the designed stochastic solver. To prove the reliability of scheme, the numerical measures are presented using correlations, error histograms, state transitions, and regression.

The dynamics of novel corona virus disease via stochastic epidemiological model with vaccination

During the past two years, the novel coronavirus pandemic has dramatically affected the world by producing 4.8 million deaths. Mathematical modeling is one of the useful mathematical tools which has been used frequently to investigate the dynamics of various infectious diseases. It has been observed that the nature of the novel disease of coronavirus transmission differs everywhere, implying that it is not deterministic while having stochastic nature. In this paper, a stochastic mathematical model has been investigated to study the transmission dynamics of novel coronavirus disease under the effect of fluctuated disease propagation and vaccination because effective vaccination programs and interaction of humans play a significant role in every infectious disease prevention. We develop the epidemic problem by taking into account the extended version of the susceptible-infected-recovered model and with the aid of a stochastic differential equation. We then study the fundamental axioms for existence and uniqueness to show that the problem is mathematically and biologically feasible. The extinction of novel coronavirus and persistency are examined, and sufficient conditions resulted from our investigation. In the end, some graphical representations support the analytical findings and present the effect of vaccination and fluctuated environmental variation.

A mathematical model of coronavirus transmission by using the heuristic computing neural networks

In this study, the nonlinear mathematical model of COVID-19 is investigated by stochastic solver using the scaled conjugate gradient neural networks (SCGNNs). The nonlinear mathematical model of COVID-19 is represented by coupled system of ordinary differential equations and is studied for three different cases of initial conditions with suitable parametric values. This model is studied subject to seven class of human population N(t) and individuals are categorized as: susceptible S(t), exposed E(t), quarantined Q(t), asymptotically diseased I_A (t), symptomatic diseased I_S (t) and finally the persons removed from COVID-19 and are denoted by R(t). The stochastic numerical computing SCGNNs approach will be used to examine the numerical performance of nonlinear mathematical model of COVID-19. The stochastic SCGNNs approach is based on three factors by using procedure of verification, sample statistics, testing and training. For this purpose, large portion of data is considered, i.e., 70%, 16%, 14% for training, testing and validation, respectively. The efficiency, reliability and authenticity of stochastic numerical SCGNNs approach are analysed graphically in terms of error histograms, mean square error, correlation, regression and finally further endorsed by graphical illustrations for absolute errors in the range of 10^-05 to 10^-07 for each scenario of the system model.

A neuro swarm procedure to solve the novel second order perturbed delay Lane-Emden model arising in astrophysics

The current work provides a mathematical second order perturbed singular delay differential model (SO-PSDDM) by using the standard form of the Lane-Emden model. The inclusive structures based on the delay terms, singular-point and perturbation factor and shape forms of the SO-PSDDM are provided. The novel form of the SO-PSDDM is numerically solved by using the procedures of artificial neural networks (ANNs) along with the optimization measures based on the swarming procedures (PSO) and interior-point algorithm (IPA). An error function is optimized through the swarming PSO procedure along with the IPA to solve the SO-PSDDM. The precision, substantiation and validation are observed for three problems of the SO-PSDDM. The exactness of the novel SO-PSDDM is observed by comparing the obtained and exact solutions. The reliability, stability and convergence of the proposed stochastic algorithms are observed for 30 independent trials to solve the novel SO-PSDDM.

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.

Solving Fredholm Integral Equations Using Deep Learning

The aim of this paper is to provide a deep learning based method that can solve high-dimensional Fredholm integral equations. A deep residual neural network is constructed at a fixed number of collocation points selected randomly in the integration domain. The loss function of the deep residual neural network is defined as a linear least-square problem using the integral equation at the collocation points in the training set. The training iteration is done for the same set of parameters for different training sets. The numerical experiments show that the deep learning method is efficient with a moderate generalization error at all points. And the computational cost does not suffer from “curse of dimensionality” problem.