Numerical Investigations of the Fractional-Order Mathematical Model Underlying Immune-Chemotherapeutic Treatment for Breast Cancer Using the Neural Networks

This study aims to solve the nonlinear fractional-order mathematical model (FOMM) by using the normal and dysregulated bone remodeling of the myeloma bone disease (MBD). For the more 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.

Section: Resultsmentioning

confidence: 99%

Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

Yotha¹,

Hiader²,

Sabir³

et al. 2023

“…Recently, stochastic solvers have been presented to solve the fractional dynamical models. Few of them are dynamical nonlinear susceptible infected and quarantine differential model [55], immune-chemotherapeutic treatment for breast cancer [56], nonlinear prey-predator system [57], SIDARTHE COVID-19 pandemic differential model [58], Bagley-Torvik mathematical model [59] and seventh order singular system [60]. It is found that the time FO derivatives have been applied to different conditions in various applications.…”

Section: Novel Stochastic Solvers Featuresmentioning

confidence: 99%

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

Botmart¹,

Hiader²,

Sabir³

et al. 2023

Self Cite

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 fading memories 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 S h (t), infected humans I h (t), recovered humans R h (t), infected vectors I v (t) , and susceptible vector S v (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.

“…The data magnitudes are implemented 75% for training, 10% for certification and 15% for testing to solve the FO-HBV-DIS with the response of antibody immune. The stochastic numerical procedures have the competence and ability to solve the linear models as well as various stiff complex nonlinear systems [42][43][44][45][46][47][48][49][50]. These numerical performances of the integer order motivated the authors to present the numerical simulations of FO derivatives of nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Procedure for Fractional HBV Infection with Impact of Antibody Immune

Noinang¹,

Sabir²,

Raja³

et al. 2023

The current investigations are presented to solve the fractional order HBV differential infection system (FO-HBV-DIS) with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation (LMB) neural networks (NNs), i.e., LMBNNs. The FO-HBV-DIS with the response of antibody immune is categorized into five dynamics, healthy hepatocytes (H), capsids (D), infected hepatocytes (I), free virus (V) and antibodies (W). The investigations for three different FO variants have been tested numerically to solve the nonlinear FO-HBV-DIS. The data magnitudes are implemented 75% for training, 10% for certification and 15% for testing to solve the FO-HBV-DIS with the response of antibody immune. The numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton approach. To authenticate the validity, competence, consistency, capability and exactness of the LMBNNs, the numerical presentations using the mean square error (MSE), error histograms (EHs), state transitions (STs), correlation and regression are accomplished.