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.