Stochastic Model For HIV Research Articles

Dynamic behavior of a stochastic HIV model with latent infection and Ornstein–Uhlenbeck process

HIV spreads in the body through two infection patterns: virus-to-cell (VTC) infection and cell-to-cell (CTC) transmission. This study introduces an HIV dynamic model incorporating both transmission patterns, where CTC transmission occurs when healthy CD4+T cells come into contact with latently and actively infected cells. The research first analyzes the local asymptotic stability of the disease-free equilibrium and the global asymptotic stability of the endemic equilibrium in the deterministic model. Subsequently, a corresponding stochastic HIV model is developed by introducing log-normal Ornstein–Uhlenbeck (OU) process to perturb the infection rates. The study establishes the conditions for the extinction of HIV infection in the stochastic system and examines the existence of an ergodic stationary distribution by constructing a series of stochastic Lyapunov functions. Specifically, the paper proposes the explicit expression of the probability density function for the linearized stochastic system near the quasi-equilibrium when all infected cells transform into latently infected cells. Finally, the theoretical conclusions are validated through numerical simulations.

Stationary distribution and near‐optimal control of a stochastic reaction–diffusion HIV model

Considering stochastic perturbations and spatial diffusion in both virus‐to‐cell and cell‐to‐cell transmissions, a stochastic reaction–diffusion HIV model is developed. Firstly, the existence and uniqueness of a global positive solution and stationary distribution are demonstrated. Secondly, considering the effect of drug therapy on the disease, the control strategy is introduced into the stochastic HIV model. By employing Pontryagin's stochastic maximum principle, the sufficient and necessary conditions are obtained for near‐optimal control. Finally, numerical simulations are reported to support and supplement our theoretical results.

Dynamics analysis of a stochastic HIV model with non-cytolytic cure and Ornstein–Uhlenbeck process

In this paper, we introduce an HIV infection model with virus-to-cell infection, cell-to-cell infection and non-cytolytic cure. Two mean-reverting Ornstein–Uhlenbeck processes are also taken into account in the model. Firstly, it is proved that the stochastic model has a unique positive global solution. The model is found to have at least one stationary distribution by constructing suitable Lyapunov functions if the critical condition R0s>1. Then, the probability density function near the quasi-positive equilibrium is obtained by solving the corresponding Fokker–Planck equation. The spectral radius method is used to derive the virus extinction under a sufficient condition R0e<1. Finally, some numerical simulations are carried out.

Dynamic Behavior of a General Stochastic HIV Model with Virus-to-Cell Infection, Cell-to-Cell Transmission, Immune Response and Distributed Delays

Dynamic Behavior of a General Stochastic HIV Model with Virus-to-Cell Infection, Cell-to-Cell Transmission, Immune Response and Distributed Delays

Analysis of a stochastic HIV model with cell-to-cell transmission and Ornstein–Uhlenbeck process

In this paper, we establish and analyze a stochastic human immunodeficiency virus model with both virus-to-cell and cell-to-cell transmissions and Ornstein–Uhlenbeck process, in which we suppose that the virus-to-cell infection rate and the cell-to-cell infection rate satisfy the Ornstein–Uhlenbeck process. First, we validate that there exists a unique global solution to the stochastic model with any initial value. Then, we adopt a stochastic Lyapunov function technique to develop sufficient criteria for the existence of a stationary distribution of positive solutions to the stochastic system, which reflects the strong persistence of all CD4+ T cells and free viruses. In particular, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-chronic infection equilibrium of the stochastic system. Finally, numerical simulations are conducted to validate these analytical results. Our results suggest that the methods used in this paper can be applied to study other viral infection models in which the infected CD4+ T cells are divided into latently infected and actively infected subgroups.

Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching

Considering the influences of uncertain factors on the reproduction of virus in vivo, a stochastic HIV model with CTLs’ immune response and logistic growth was developed to research the dynamics of HIV, where uncertain factors are white noise and telegraph noise. which are described by Brownian motion and Markovian switching, respectively. We show, firstly, the existence of global positive solutions of this model. Further, by constructing suitable stochastic Lyapunov functions with regime switching, some sufficient conditions for the existence and uniqueness of the stationary distribution and the conditions for extinction are obtained. Finally, the main results are explained by some numerical examples. Theoretical analysis and numerical simulation show that low-intensity white noise can maintain the persistence of the virus, and high intensity white noise can make the virus extinct after a period of time with multi-states.

Stochastic HIV model coupled with pharmacokinetics and drug adherence may explain intermittent viral blips

We develop a stochastic HIV model by integrating drug adherence into a pharmacokinetic model and by coupling a pharmacodynamic model with a viral dynamic model. Numerical simulations show that the proposed model can generate viral blips, which have been observed in HIV patients receiving suppressive antiretroviral therapy. We calculate the probability density function of infected CD4+ T cells by developing the generalized density evolution equation. We fit the model to the clinical data of four HIV patients exhibiting viral blips. The results demonstrate that poor drug adherence can be a reason explaining the occurrence of viral blips in treated HIV patients. We also find that viral dynamics are sensitive to drug-adherence parameters, which have a significant impact on the frequency and amplitude of viral blips. The modeling and methods can be applied to the study of long-term therapy of other chronic diseases in which drug adherence might also be an issue.

Stationary distribution, extinction and density function for a stochastic HIV model with a Hill-type infection rate and distributed delay

&lt;abstract&gt;&lt;p&gt;In this article, we investigate the dynamics of a stochastic HIV model with a Hill-type infection rate and distributed delay, which are better choices for mass action laws. First, we transform a stochastic system with weak kernels into a degenerate high-dimensional system. Then the existence of a stationary distribution is obtained by constructing a suitable Lyapunov function, which determines a sharp critical value $ R_0^s $ corresponding to the basic reproduction number for the determined system. Moreover, the sufficient condition for the extinction of diseases is derived. More importantly, the exact expression of the probability density function near the quasi-equilibrium is obtained by solving the Fokker-Planck equation. Finally, numerical simulations are illustrated to verify the theoretical results.&lt;/p&gt;&lt;/abstract&gt;

The impact of nonlinear perturbation to the dynamics of HIV model

In this paper, we developed and studied a stochastic HIV model with nonlinear perturbation. Through a rigorous analysis, we firstly showed that the solution of the stochastic model is positive and global. Then, by employing suitable stochastic Lyapunov functions, we prove that the stochastic model admit a unique ergodic stationary distribution. In addition, sufficient conditions for the extinction of HIV infection are derived. Finally, numerical simulations are employed to confirm our theoretical results.

An HIV latent infection model with cell-to-cell transmission and stochastic perturbation

During the HIV infection process in vitro cell cultures, recent experimental and mathematical investigations have revealed that there are two fundamentally distinct viral transmission modes: cell-free infection and cell-to-cell transmission. A stochastic HIV model with latent infection, cell-free infection and cell-to-cell transmission is formulated in this paper. The existence of the unique ergodic stationary distribution is established by constructing appropriate Lyapunov function. Moreover, virus can be eradicated under certain sufficient conditions. Numerical simulations are carried out to investigate three aspects: (i) the effect of stochastic perturbation; (ii) the influence of latency; (iii) the relative contributions of cell-to-cell and cell-free infections.

Stationary distribution and probability density function analysis of a stochastic HIV model with cell-to-cell infection

In this paper, a stochastic HIV model with CD4+ T-cell proliferation, cell-free infection and cell-to-cell transmission is proposed. By constructing suitable Lyapunov function, we establish the existence of unique and ergodic stationary distribution of the model. Moreover, by using asymptotic analysis and employing the Fokker-Planck equation, we derive the probability density function around the quasi-steady state of the system. Through numerical simulations, the effects of the stochastic perturbation and cell-to-cell infection on model dynamic behavior are investigated, thus the probability density function of the system is also given under the realistic parameter values.

Asymptotic behavior of a stochastic HIV model with Beddington\u2013DeAngelis functional response

In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.

Stationary distribution of a stochastic HIV model with two infective stages

A stochastic HIV model is studied in this paper. Using the Lyapunov analysis method, we provide a sufficient condition for the ergodic stationary distribution of the positive solutions to the model.

A stochastic delay model of HIV pathogenesis with reactivation of latent reservoirs

Abstract In this paper, we propose a stochastic HIV model with latency to describe the factors that are responsible for extinction and persistence of the infection. This model incorporates latent period of reservoirs that inhibits the eradication of the virus. It is shown that this model leads naturally to a stochastic system of differential delay equations. We derived the global existence, positivity and boundedness properties of solutions of the proposed stochastic system. Analyzing the model, sufficient conditions for the eradication and the persistence of the disease are also obtained. Furthermore, numerical simulations are performed to study the impact of several strategies of drug therapy on the persistence and the extinction of HIV virus. Our results constitute an important step towards control strategies to reduce HIV infection.

Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function

A stochastic HIV viral model with both logistic target cell growth and nonlinear immune response function is formulated to investigate the effect of white noise on each population. The existence of the global solution is verified. By employing a novel combination of Lyapunov functions, we obtain the existence of the unique stationary distribution for small white noises. We also derive the extinction of the virus for large white noises. Numerical simulations are performed to highlight the effect of white noises on model dynamic behaviour under the realistic parameters. It is found that the small intensities of white noises can keep the irregular blips of HIV virus and CTL immune response, while the larger ones force the virus infection and immune response to lose efficacy.