A stochastic model for internal HIV dynamics

In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and find out the mean and variance of this process. Numerical simulations conclude the paper.

[1]  N Dalal.  Applications of stochastic and ordinary differential equations to HIV dynamics. , 2006 .

[2]  C. Braumann,et al.  Variable effort harvesting models in random environments: generalization to density-dependent noise intensities. , 2002, Mathematical biosciences.

[3]  A. Perelson,et al.  HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time , 1996, Science.

[4]  Patrick W Nelson,et al.  Mathematical analysis of delay differential equation models of HIV-1 infection. , 2002, Mathematical biosciences.

[5]  Alan S. Perelson,et al.  Increased Turnover of T Lymphocytes in HIV-1 Infection and Its Reduction by Antiretroviral Therapy , 2001, The Journal of experimental medicine.

[6]  Alan S Perelson,et al.  HIV-1 infection and low steady state viral loads , 2002, Bulletin of mathematical biology.

[7]  M A Nowak,et al.  Anti-viral drug treatment: dynamics of resistance in free virus and infected cell populations. , 1997, Journal of theoretical biology.

[8]  A. Perelson,et al.  Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay. , 2004, Journal of theoretical biology.

[9]  Richard A. Lempicki,et al.  Identification of Dynamically Distinct Subpopulations of T Lymphocytes That Are Differentially Affected by HIV , 2001, The Journal of experimental medicine.

[10]  Wanbiao Ma,et al.  Asymptotic properties of a HIV-1 infection model with time delay , 2007 .

[11]  M A Nowak,et al.  Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Davide Verotta,et al.  Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials. , 2002, Mathematical biosciences.

[13]  X. Mao,et al.  Environmental Brownian noise suppresses explosions in population dynamics , 2002 .

[14]  A. Perelson,et al.  A model of HIV-1 pathogenesis that includes an intracellular delay. , 2000, Mathematical biosciences.

[15]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[16]  V. Jansen,et al.  The dual role of CD4 T helper cells in the infection dynamics of HIV and their importance for vaccination. , 2002, Journal of theoretical biology.

[17]  H C T,et al.  A Stochastic Model for Early HIV-1 Population Dynamics , 1998 .

[18]  A A Ding,et al.  Relationships between antiviral treatment effects and biphasic viral decay rates in modeling HIV dynamics. , 1999, Mathematical biosciences.

[19]  Ruy M Ribeiro,et al.  Modeling the long-term control of viremia in HIV-1 infected patients treated with antiretroviral therapy. , 2004, Mathematical biosciences.

[20]  The Effects of Immunity and Resistance on the Development of AIDS , 2007 .

[21]  J. B. Walsh,et al.  An introduction to stochastic partial differential equations , 1986 .

[22]  X. Mao,et al.  A stochastic model of AIDS and condom use , 2007 .

[23]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[24]  D M Bortz,et al.  Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models. , 2006, Mathematical biosciences.

[25]  Xuerong Mao,et al.  Stochastic differential delay equations of population dynamics , 2005 .

[26]  H. Tuckwell,et al.  Nature of equilibria and effects of drug treatments in some simple viral population dynamical models. , 2000, IMA journal of mathematics applied in medicine and biology.

[27]  M A Nowak,et al.  Virus dynamics and drug therapy. , 1997, Proceedings of the National Academy of Sciences of the United States of America.