Stochastic numerical technique for solving HIV infection model of CD4 + T cells
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Stochastic numerical technique for solving HIV infection model of CD4+ T cells Muhammad Umar1,a , Zulqurnain Sabir1,b , Fazli Amin1,c , Juan L. G. Guirao2,d , Muhammad Asif Zahoor Raja3,4,e 1 Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan 2 Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de
Marina, 30203 Cartagena, Spain
3 Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus,
Attock 43600, Pakistan
4 Present Address: Future Technology Research Center, National Yunlin University of Science and
Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, People’s Republic of China
Received: 5 July 2019 / Accepted: 24 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The intension of the present work is to present the stochastic numerical approach for solving human immunodeficiency virus (HIV) infection model of cluster of differentiation 4 of T-cells, i.e., CD4+ T cells. A reliable integrated intelligent computing framework using layered structure of neural network with different neurons and their optimization with efficacy of global search by genetic algorithms supported with rapid local search methodology of active-set method, i.e., hybrid of GA-ASM, is used for solving the HIV infection model of CD4+ T cells. A comparison between the present results for different neurons-based models and the numerical values of the Runge–Kutta method reveals that the present intelligent computing techniques is trustworthy, convergent and robust. Statistics-based observation on different performance indices further demonstrates the applicability, effectiveness and convergence of the present schemes. 1 Introduction In recent years, numerous mathematical models have been built-up for human immunodeficiency virus (HIV) infectious dynamics of cluster of differentiation 4 of T-cells, i.e., CD4+ T cells. The present study is about the HIV infection model [1]. This model is the combination of three basic component models, which are CD4+ T cells septic by the HIV viruses, attention of susceptible cells and free HIV virus elements in the blood. The general form of the model is a system of three nonlinear system of differential equations, written as [1]:
a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] d e-mail: [email protected] (corresponding author) e e-mail: [email protected]
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Eur. Phys. J. Plus
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⎧ ⎪ dT r T 1 − T +I − αT + q − kV T, T (0) r , ⎪ ⎪ 1 ⎪ T max ⎪ ⎨ dt d I −β I + kV T, I (0) r2 , ⎪ dt ⎪ ⎪ ⎪ ⎪ ⎩ dV −γ V + nβ I, V (0) r3 , dt
(1)
where T (t), I (t) and V (t) represent the concentration of CD4+ T cells, septic from the viruses of HIV and virus free particles, respectively. Furthermore, r, Tmax , q, k and n, respectively, denote growth rate of CD4+ T cell concentration, maximal attent
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