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

Wang, Yan; Qi, Kai; Jiang, Daqing

doi:10.1016/j.chaos.2021.111215

Cited by 10 publications

(7 citation statements)

References 52 publications

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“…However, from the viewpoint of microscopic, the interference of random factor exists in the process of virus replication [22]. In order to take into account some crucial epidemiological factors such as, antiretroviral (ART) therapy, infection mechanism in heterogeneous environment, etc., many scholars have developed various stochastic differential equations (SDEs) models, specially stochastic ordinary differential equations models [22,23,24,25,26,27] to study the pathogenesis and replication process of HIV/AIDS. For example, Lu et al [22] analyzed the stationary distribution and probability density of a stochastic HIV model with cell-to-cell transmission.…”

Section: Parameters Descriptions λmentioning

confidence: 99%

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

Liu

2023

Journal of Mathematical Physics

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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.

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Section: Parameters Descriptions λmentioning

confidence: 99%

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

Liu

2023

Journal of Mathematical Physics

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“…For some problems in their work, controllers are obtained using the dynamic programming method. There is already lots of work on HIV models with and without age structure; more details can be found in previous studies [15][16][17][18][19][20][21][22][23][24][25]. Also, for the work related to optimal control problems in structured or unstructured population models, we refer to previous studies [4,14,26,27].…”

Section: Introductionmentioning

confidence: 99%

Stability and optimal control of age‐structured cell‐free and cell‐to‐cell transmission model of HIV

Kumar

Abbas

2023

Math Methods in App Sciences

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The human immunodeficiency virus (HIV) can spread more efficiently when infected CD4+ T cells directly interact with uninfected T cells. This interaction forms virological synapses, which lead to the cell‐to‐cell transmission of HIV. This study considers an age‐structured HIV infection model in which both cell‐free infection and cell‐to‐cell transmission occur. We also incorporate the proportion of T cells in latent or exposed class. Equilibrium solutions to our model are derived and then we perform the stability analysis. Optimal control problem for the drug therapy is also considered. Forward–backward scheme is used to solve the optimal control problem numerically. Numerical simulation added to study the effect of cell‐to‐cell infection. The outcomes of this work are new and complement the existing ones.

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“…The mechanism of HIV transmission has been modeled and numerically simulated in many literatures. [3][4][5][6][7][8][9] Specifically, Silva and Torres 4 proposed a nonlinear mathematical model for HIV/AIDS transmission with varying population size in a homogeneously mixing population and proved the global stability of the endemic equilibrium. Furthermore, Wang et al 6 studied the corresponding stochastic model and established sufficient conditions of the extinction and persistence in mean for the disease.…”

Section: Introductionmentioning

confidence: 99%

“…The mechanism of HIV transmission has been modeled and numerically simulated in many literatures 3–9 . Specifically, Silva and Torres 4 proposed a nonlinear mathematical model for HIV/AIDS transmission with varying population size in a homogeneously mixing population and proved the global stability of the endemic equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior and density function analysis of a stochastic HIV/AIDS model with general incidence rate

Zhang

Yang

Wang

2022

Math Methods in App Sciences

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In this paper, we mainly present the dynamic properties of a stochastic SICA model with general incidence rate. Through rigorous analysis and reasoning of the stochastic model, we obtain that the solution of the model is global, positive, and unique. By constructing the threshold value R s 0 , which includes the influence of white noise, we obtain a sufficient condition for the ergodicity of this model. Furthermore, we show that the model has a unique ergodic stationary distribution while R s 0 > 1 by adopting a novel method. The extinction of the system is also established. Besides, the expression of probability density function of the stochastic model with bilinear incidence rate around the unique stable positive equilibrium of the deterministic model is derived. Finally, numerical simulations are presented to illustrate the theoretical results.

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

Cited by 10 publications

References 52 publications

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

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

Stability and optimal control of age‐structured cell‐free and cell‐to‐cell transmission model of HIV

Dynamical behavior and density function analysis of a stochastic HIV/AIDS model with general incidence rate

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