The Stochastic Stability of Internal HIV Models with Gaussian White Noise and Gaussian Colored Noise

Abstract

In this paper, the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise is analyzed. First, the stability of deterministic models is investigated. By analyzing the characteristic values of endemic equilibrium, we could obtain that internal HIV models reach a steady state under the influence of RTI and PI drugs. Then we discuss the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise, based on probability density functions. The functional methods are carried out to derive the approximate Fokker-Planck equation of stochastic internal HIV systems and further obtain the marginal probability density functions. Finally, numerical results show that the noise intensities have a great influence on uninfected cell, infected cell, and virus particles, for predicting the stability of stochastic dynamic systems subjected to Gaussian white noise and Gaussian colored noise.

Phase Congruential White Noise Generator

“…It should be emphasized that the congruential generator only works with an integer number of bits. From Expression (34) it follows that a quantity of Fourier frequencies should correspond to the following power function:…”

“…An analysis of the literature shows that most of the articles describe different applications of white noise, as well as its recognition in transmitted signals. This includes the areas such as theoretical and applied mathematics [5][6][7][8][9], physical research [3,4,[10][11][12][13], electronic and radio engineering [14][15][16][17][18][19][20][21][22][23], acoustics and noise phenomena [1][2][3][4]24,25], computer algorithms [26,27], geological prospecting and exploration [28,29], medical and biological research [30][31][32][33][34][35][36], psychology and psychiatry [37,38], and others. It is worth noting that significant results have been achieved in those fields.…”

Stochastic Analysis of Predator–Prey Models under Combined Gaussian and Poisson White Noise via Stochastic Averaging Method

“…Thus, an important task here is to obtain the PDFs for both prey and predator population densities. In this paper, we focus on the longterm behavior of this stochastic model, namely, the stationary responses of Equation (14). To derive the stationary PDFs, we use a stochastic averaging method as described below.…”

“…Moreover, the evolution of real-world biological systems usually suffers from unavoidable random perturbations in the natural environment [5][6][7][8][9]. Many investigations on the dynamics of predator-prey models with predator saturation and predator competition terms excited by stochastic perturbations have been reported [8][9][10][11][12][13][14]. In these studies, the stochastic perturbation is introduced as continuous stochastic excitations to disturb the birth rate of the prey and the death rate of the predator.…”

A near analytic solution of a stochastic immune response model considering variability in virus and T cell dynamics

“…Taking this variability and population heterogeneity into consideration, a few stochastic immune response models have been developed in the recent past [15][16][17]. Dalal et al in their work introduced stochasticity in the deterministic model of immune response in HIV infection by parameter perturbation [15].…”