Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

This study aims to solve the nonlinear fractional-order mathematical model(FOMM)by using the normal and dysregulated bone remodeling of themyeloma bone disease(MBD).For themore precise performance of the model,fractional-order derivatives have been used to solve the disease model numerically.The FOMM is preliminarily designed to focus on the critical interactions between bone resorption or osteoclasts(OC)and bone formation or osteoblasts(OB).The connections of OC and OB are represented by a nonlinear differential system based on the cellular components,which depict stable fluctuation in the usual bone case and unstable fluctuation through the MBD.Untreated myeloma causes by increasing the OC and reducing the osteoblasts,resulting in net bone waste the tumor growth.The solutions of the FOMM will be provided by using the stochastic framework based on the Levenberg-Marquardt backpropagation(LVMBP)neural networks(NN),i.e.,LVMBPNN.The mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the LVMPNN.The static structural performances are 82%for investigation and 9%for both learning and certification.The performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton mechanism.To accomplish the capability,steadiness,accuracy,and ability of the LVMBPNN,the performances of the error histograms(EHs),mean square error(MSE),recurrence,and state transitions(STs)will be provided.

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system(VHDNS)along with the numerical treatment of artificial neural networks(ANNs)techniques supported by Levenberg-Marquardt backpropagation(LMQBP),known as ANNs-LMQBP.This mechanism is physically appropriate,where the number of infected people is increasing along with the limited health services.Furthermore,the biological effects have fadingmemories and exhibit transition behavior.Initially,the model is developed by considering the two and three categories for the humans and the vector species.The VHDNS is constructed with five classes,susceptible humans Sh(t),infected humans Ih(t),recovered humans Rh(t),infected vectors Iv(t),and susceptible vector Sv(t)based system of the fractional-order nonlinear ordinary differential equations.To solve the number of variations of the VHDNS,the numerical simulations are performed using the stochastic ANNs-LMQBP.The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training,verifying,and testing data to decrease the mean square error(MSE).An extensive analysis is provided using the correlation studies,MSE,error histograms(EHs),state transitions(STs),and regression to observe the accuracy,efficiency,expertise,and aptitude of the computing ANNs-LMQBP.

Dynamics of Fractional Differential Model for Schistosomiasis Disease

In the present study,a design of a fractional order mathematical model is presented based on the schistosomiasis disease.To observe more accurate performances of the results,the use of fractional order derivatives in the mathematical model is introduce based on the schistosomiasis disease is executed.The preliminary design of the fractional order mathematical model focused on schistosomiasis disease is classified as follows:uninfected with schistosomiasis,infected with schistosomiasis,recovered from infection,susceptible snail unafflicted with schistosomiasis disease and susceptible snail afflicted with this disease.The solutions to the proposed system of the fractional order mathematical model will be presented using stochastic artificial neural network(ANN)techniques in conjunction with the LevenbergMarquardt backpropagation(LMBP),referred to as ANN-LMBP.To illustrate the preciseness of the ANN-LMBP method,mathematical presentations of three different values focused on fractional order will be performed.These statics performances are taken in these investigations are 78%and 11%for both learning and certification.The accuracy of the ANN-LMBP method is determined by comparing the values obtained by the database Adams-Bash forth-Moulton scheme.The simulation-based error histograms(EHs),MSE,recurrence,and state transitions(STs)will be offered to achieve the capability,accuracy,steadiness,abilities,and finesse of the ANN-LMBP method.