# American Institute of Mathematical Sciences

## Solving a class of biological HIV infection model of latently infected cells using heuristic approach

 1 Department of Dermatology, Stomatology, Radiology and Physical Medicine, University of Murcia, Spain 2 Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan 3 Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203-Cartagena, Región de Murcia, Spain 4 Department of Electrical and Computer Engineering, COMSATS University, Islamabad, Attock Campus, Attock, Pakistan

* Corresponding author: Yolanda Guerrero–Sánchez

Received  September 2019 Revised  December 2019 Published  November 2020

The intension of the recent study is to solve a class of biological nonlinear HIV infection model of latently infected CD4+T cells using feed-forward artificial neural networks, optimized with global search method, i.e. particle swarm optimization (PSO) and quick local search method, i.e. interior-point algorithms (IPA). An unsupervised error function is made based on the differential equations and initial conditions of the HIV infection model represented with latently infected CD4+T cells. For the correctness and reliability of the present scheme, comparison is made of the present results with the Adams numerical results. Moreover, statistical measures based on mean absolute deviation, Theil's inequality coefficient as well as root mean square error demonstrates the effectiveness, applicability and convergence of the designed scheme.

Citation: Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020431
##### References:

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##### References:
Graphical illustration of presented scheme for HIV infection model of latently infected cells
Pseudo code using PSO-IPA
Trained weights or decision variables of ANN on the basis of best fitness achieved
Results for HIV infection spread model
Comparative study on AE of the presented solutions using 5 neurons with the Adams results
Analysis on MAD for convergence along with the histograms for 5 neurons
Analysis on RMSE for convergence along with the histograms for 5 neurons
Analysis on TIC for convergence along with the histograms for 5 neurons
Statistics based results of Problem 1 for $x(t)$ and $w(t)$
Statistics based results of Problem 1 for $y(t)$ and $\nu(t)$
List of parameter and setting used for reported study of HIV infection model
 Index Description Settings [8] $S_{1}$ Initial value of uninfected CD4+T cells 7 $S_{2}$ Initial value of infected CD4+T cells 2 $S_{3}$ Initial value of Virus free cells 1 $S_{4}$ Initial value of latently infected cells 4 $\mu$ Rate of uninfected CD4+T cells 0.4 $\lambda$ Recovery Rate of infected cells 0.3 $d$ Death rate of uninfected CD4+T cells 0.01 $\alpha$ Rate of infection spread 0.04 $q$ Rate of removal of recombinants 0.1 $a$ Death rate of virus free cells 0.2 $u$ Death rate of latently infected cells 0.03
 Index Description Settings [8] $S_{1}$ Initial value of uninfected CD4+T cells 7 $S_{2}$ Initial value of infected CD4+T cells 2 $S_{3}$ Initial value of Virus free cells 1 $S_{4}$ Initial value of latently infected cells 4 $\mu$ Rate of uninfected CD4+T cells 0.4 $\lambda$ Recovery Rate of infected cells 0.3 $d$ Death rate of uninfected CD4+T cells 0.01 $\alpha$ Rate of infection spread 0.04 $q$ Rate of removal of recombinants 0.1 $a$ Death rate of virus free cells 0.2 $u$ Death rate of latently infected cells 0.03
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