Numerical Treatment of Non-Linear System for Latently Infected CD4+T Cells: A Swarm- Optimized Neural Network Approach

Abstract

Swarm-inspired computing techniques are the best candidates for solving various nonlinear problems. The current study aims to exploit the swarm intelligence technique known as Particle Swarm Optimization (PSO) for the numerical investigation of a nonlinear system of latently infected CD4+T cells. The strength of the Mexican Hat Wavelet (MHW) based unsupervised Feed Forward Artificial Neural Network (FFANN) is used to solve the nonlinear system of latently infected CD4+T cells. The function approximation of unsupervised ANN is used to construct the mathematical model of the latently infected CD4+T cells by defining the error function in the mean square manner. The adjustable parameters called the unknowns of the network are optimized by using the Particle Swarm Optimization (PSO), Nedler Mead Simplex Method (NMSM), and their hybrid PSO-NMSM. The PSO applied for the global optimization of weights aided by the NMSM algorithm for rapid local search. Finally, a Comprehensive Monte Carlo simulation and statistical analysis of the analytical method, numerical Range Kutta (RK) method, ANN optimized with Genetic Algorithm (GA) aided with Sequential Quadratic Programming (SQP) known as GA-SQP, ANN-PSO-SQP and the proposed MHW-HIVFFANN-PSO-NMSM are performed to validate the effectiveness, stability, convergence, and computational complexity of each scheme. It is observed that the proposed MHW-FFANN-HIVPSO-NMSM scheme has converged in all classes at $10~^{-6}$ , $10^{-7}$ , and $10~^{-8}$ and solved the nonlinear system of latently infected CD4+ T cells more accurately and effectively. The absolute error lies in $10^{-3}$ , $10^{-4}$ , $10^{-4}$ , and $10^{-5}$ for numerical, ANN-GA-SQP, ANN-PSO-SQP, and proposed MHW-ANN-PSO-NMSM respectively. Moreover, the proposed scheme is stable for the large number of independent runs. The values for global statistical indicators’ global mean squared error are lies 8.15E-09, 3.25E-10, 4.15E-09, and 3.15E-10 for class X(t), W(t), Y(t), and V(t) respectively whereas the global mean absolute deviation lies in range 7.35E-09, 8.50E-10, 2.10E-10 and 7.10E-09.

Keywords

• Mathematical modeling
• artificial neural network
• hybrid optimization
• nonlinear system of latently infected CD4+ T cells
• Monte Carlo simulations
• ANN-based numerical treatment