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This paper is devoted to the study of the stability of a CD 4 + T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value ℛ 0 ≤ 1 ; the endemic equilibrium is globally asymptotically stable if ℛ 0 > 1 and d u ∗ − δ w ∗ ≥ 0. Finally, we give an application and numerical simulations to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this work, biologically-inspired computing framework is developed for HIV infection of CD4 T-cell model using feed-forward artificial neural networks (ANNs), genetic algorithms (GAs), sequential quadratic programming (SQP) and hybrid approach based on GA-SQP. The mathematical model for HIV infection of CD4 T-cells is represented with the help of initial value problems (IVPs) based on the system of ordinary differential equations (ODEs). The ANN model for the system is constructed by exploiting its strength of universal approximation. An objective function is developed for the system through unsupervised error using ANNs in the mean square sense. Training with weights of ANNs is carried out with GAs for effective global search supported with SQP for efficient local search. The proposed scheme is evaluated on a number of scenarios for the HIV infection model by taking the different levels for infected cells, natural substitution rates of uninfected cells, and virus particles. Comparisons of the approximate solutions are made with results of Adams numerical solver to establish the correctness of the proposed scheme. Accuracy and convergence of the approach are validated through the results of statistical analysis based on the sufficient large number of independent runs. [ABSTRACT FROM AUTHOR]

The HIV infection model of CD4T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials (OBPs). By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton's method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods. [ABSTRACT FROM AUTHOR]