Evolution dynamics of a time-delayed reaction–diffusion HIV latent infection model with two strains and periodic therapies

Wu, Peng; Zheng, Song; He, Ze-Rong

doi:10.1016/j.nonrwa.2022.103559

Cited by 10 publications

(9 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the paper, they assumed the drug efficacy function is periodic, which is characterized by a quick rise to a maximum soon after drug intake. Afterwards, Wu et al [21] investigated the evolution dynamics of a time delays heterogeneity spatial diffusion HIV latent infection model with periodic therapies and two strains. However, the above research works just consider the constant time delay, few time-dependent periodic delays spatial heterogeneity diffusion models are formulated to investigate the infection process of HIV within the host.…”

Section: P Wumentioning

confidence: 99%

“…In clinical treatment, antiviral therapy can directly address every step of virus replication and infection, thereby interrupting the replication and spread of the virus. Due to the periodicity of antiviral treatment, we can assume that all parameters of the model are continuous function with a time t period of 12h [25].…”

Section: Model Simulationmentioning

confidence: 99%

“…To this end, we first assume the bounded domain Ω = (0, π) for simplicity. To describe the periodic of the HAART treatment, as similar arguments those in [21], we can assume some parameters in system (2.5) have the following form…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Here, the biological meaning of η k , k = {II, F I, RT, R5, P I, IF I} can be found in Sect.2 [21] for details. The values of η k are choose as in [21] η P I (t) = 0.9 − 0.…”

Section: Numerical Simulationsmentioning

confidence: 99%

See 3 more Smart Citations

Modeling and analysis of a periodic delays spatial diffusion HIV model with three-stage infection process

Wu,

2024

Int. J. Biomath.

View full text Add to dashboard Cite

Considering the antiviral drugs can act on the fusion, reverse transcription, and budding stages of HIV infected cells, in this paper, we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-stage infection process to study the effects of periodic antiviral treatment and spatial heterogeneity on HIV infection process. We first study the well-posedness of the full system and then derive the basic reproduction number [Formula: see text], which is defined as the spectral radius of the next generation operator. We further prove that [Formula: see text] is a threshold for the elimination and persistence of HIV infection by comparison principle and persistence theory for non-autonomous system. In the spatial homogeneous case, the explicit expression of [Formula: see text] is derived and the global attractivity of the positive steady state is proved by using the fluctuation method. Some numerical simulations are conducted to illustrate the theoretical results and our works suggest that both spatial heterogeneity and periodic delays caused by periodic antiviral therapy have a remarkable impact on the progression of HIV infection and should not be overlooked in clinical treatment process.

show abstract

Section: P Wumentioning

confidence: 99%

Section: Model Simulationmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

“…Here, the biological meaning of η k , k = {II, F I, RT, R5, P I, IF I} can be found in Sect.2 [21] for details. The values of η k are choose as in [21] η P I (t) = 0.9 − 0.…”

Section: Numerical Simulationsmentioning

confidence: 99%

See 2 more Smart Citations

Modeling and analysis of a periodic delays spatial diffusion HIV model with three-stage infection process

Wu,

2024

Int. J. Biomath.

View full text Add to dashboard Cite

show abstract

“…Recently, using mathematical modeling to study the replication process and transmission dynamics of HIV infection has been a hot research issue in the field of epidemiology [4]. Earlier studies only focus on the healthy CD4 + T cells, the infected CD4 + T cells and the free virus particles, that is virus-to-cell infection [5,6,7,8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

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

Liu

2023

Journal of Mathematical Physics

View full text Add to dashboard Cite

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.

show abstract

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Wu,

Salmaniw,

Wang

2024

J. Math. Biol.

Self Cite

View full text Add to dashboard Cite

Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number $${\mathcal {R}}_0$$ R 0 and show that the disease-free periodic solution is globally attractive when $${\mathcal {R}}_0<1$$ R 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when $${\mathcal {R}}_0>1$$ R 0 > 1 . Moreover, we find that $${\mathcal {R}}_0$$ R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

show abstract

Evolution dynamics of a time-delayed reaction–diffusion HIV latent infection model with two strains and periodic therapies

Cited by 10 publications

References 31 publications

Modeling and analysis of a periodic delays spatial diffusion HIV model with three-stage infection process

Modeling and analysis of a periodic delays spatial diffusion HIV model with three-stage infection process

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

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Contact Info

Product

Resources

About