Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response

Wang, Xiaoqin; Tan, Yiping; Cai, Yongli; Wang, Kaifa; Wang, Weiming

doi:10.3934/mbe.2021034

Cited by 16 publications

(8 citation statements)

References 32 publications

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“…In the next theorem, we will prove the existence and uniqueness of a global positive solution of the system (2). This approach has recently been used in many papers for the analysis of stochastic predator-prey systems [23][24][25][26][27], stochastic epidemic models [28][29][30][31][32][33][34] and stochastic eco-epidemiological models [35].…”

Section: Dynamics Of the Stochastic Modelmentioning

confidence: 99%

Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps

El-Shahed

Al-Nujaiban

Abdel-Baky

2022

Axioms

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This paper deals with the mathematical modelling of the red palm weevil (RPW), Rhynchophorus ferrugineus (Olivier) (Coleoptera: Curculionidae), in date palms using chemical control by utilizing injection and sex pheromone traps. A deterministic and stochastic model for RPW is proposed and analyzed. The existence of a positive global solution for the stochastic RPW model is investigated, and the conditions for the extinction of RPWs from the stochastic system are obtained. The adequate criteria for the presence of a unique ergodic stationary distribution for the RPW system are established by creating suitable Lyapunov functions. The impact of chemical injection and pheromone traps on RPW is demonstrated. The importance of environmental noise on RPW is highlighted and simulated using the Milstein method.

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Section: Dynamics Of the Stochastic Modelmentioning

confidence: 99%

Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps

El-Shahed

Al-Nujaiban

Abdel-Baky

2022

Axioms

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“…These two kinds of cells play extremely important roles in antiviral responses. There are many mathematical models formulated to study the within-host virus dynamics with and without an immune response in recent studies [1][2][3][4][5][6]. Furthermore, there are many studies considering age-structure [7,8] or reaction-diffusion [9,10] in virus dynamics.…”

Section: Introductionmentioning

confidence: 99%

Bistability and Robustness for Virus Infection Models with Nonmonotonic Immune Responses in Viral Infection Systems

Wang

2022

Mathematics

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Recently, bistable viral infection systems have attracted increased attention. In this paper, we study bistability and robustness for virus infection models with nonmonotonic immune responses in viral infection systems. The results show that the existing transcritical bifurcation undergoes backward or forward bifurcation in viral infection models with nonmonotonic immune responses. Our investigation demonstrates that the backward bifurcation threshold is the elite control threshold. When the immune intensity is greater than the elite control threshold, the virus will be under elite control; when the immune intensity is less than the elite control threshold, the virus may rebound. We also give a new definition of robustness to characterize bistable systems.

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“…Based on this, researchers start to add the white noise to the model and use stochastic differential equations (SDEs) to describe new models. 5,9,[26][27][28] Zhang et al 6 discuss the dynamical behavior of stochastic SVIR model and give sufficient conditions for the existence of nontrivial solutions in periodic parameters. Zhao and Jiang 7 investigate a stochastic SVIR epidemic model and derive the stationary distribution if defined critical value R 0 > 1.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is obvious that the systems above are subject to the environmental noise, which indicates the epidemic model described by ODE is insufficient. Based on this, researchers start to add the white noise to the model and use stochastic differential equations (SDEs) to describe new models 5,9,26‐28 . Zhang et al 6 discuss the dynamical behavior of stochastic SVIR model and give sufficient conditions for the existence of nontrivial solutions in periodic parameters.…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution and density function analysis of stochastic susceptible‐vaccinated‐infected‐recovered (SVIR) epidemic model with vaccination of newborns

Dai

Zhou

Jiang

et al. 2021

Math Methods in App Sciences

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Birth vaccinations are becoming more common in society. In this paper, we describe the developed stochastic susceptible‐vaccinated‐infected‐recovered (SVIR) epidemic model with vaccination of newborns that enable us to concern the stationary distribution and further density function. By constructing a series suitable Lyapunov function, we derive the sufficient conditions of the existence and uniqueness of an ergodic stationary distribution. More importantly, under the same conditions, we creatively find further the density function which is based on solving corresponding Fokker–Planck equation. The results of numerical simulation, which is supported by pertussis disease data, show that our conclusion accords with reality. The density function throws light on the property of an epidemic after being stationary and furnishes more information about the disease.

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Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response

Cited by 16 publications

References 32 publications

Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps

Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps

Bistability and Robustness for Virus Infection Models with Nonmonotonic Immune Responses in Viral Infection Systems

Stationary distribution and density function analysis of stochastic susceptible‐vaccinated‐infected‐recovered (SVIR) epidemic model with vaccination of newborns

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