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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.

Let i ≥ 2, ∆ ≥ 0, 1 ≤ a ≤ b − ∆, n > (a+b)(ib+2m−2) a + n and δ(G) ≥ b 2 a + n + 2m, and let g, f be two integer-valued functions defined on V (G) such that a ≤ g(x) ≤ f (x) − ∆ ≤ b − ∆ for each x ∈ V (G). In this article, it is determined that G is a fractional (g, f, n , m)-critical deleted graph if max{d 1 , d 2 , • • • , d i } ≥ b(n+n) a+b for any independent subset {x 1 , x 2 ,. .. , x i } ⊆ V (G). The result is tight on independent set degree condition.

The aim of the present paper is to state a simplified nonlinear mathematical model to describe the dynamics of the novel coronavirus (COVID-19). The design of the mathematical model is described in terms of four categories susceptible ([Formula: see text], infected ([Formula: see text], treatment ([Formula: see text] and recovered ([Formula: see text], i.e. SITR model with fractals parameters. These days there are big controversy on if is needed to apply confinement measure to the population of the word or if the infection must develop a natural stabilization sharing with it our normal life (like USA or Brazil administrations claim). The aim of our study is to present different scenarios where we draw the evolution of the model in four different cases depending on the contact rate between people. We show that if no confinement rules are applied the stabilization of the infection arrives around 300 days affecting a huge number of population. On the contrary with a contact rate small, due to confinement and social distancing rules, the stabilization of the infection is reached earlier.

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