Periodic behavior in a FIV model with seasonality as well as environment fluctuations

Wang, Weiming; Cai, Yongli; Li, Jingyuan; Gui, Zhanji

doi:10.1016/j.jfranklin.2017.08.034

Cited by 57 publications

(20 citation statements)

References 40 publications

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“…The medica coverage as an effective preventive measure plays an important role in controlling the disease spread [4]. Dynamical modeling of infectious disease has become a powerful tool to improve our understanding of the pattern of epidemic spread and develop better controlling strategies [41]. Meanwhile, in real situation, the environmental fluctuation should not be ignored.…”

Section: Discussionmentioning

confidence: 99%

The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model

Zhao

Zhang

Yuan

2018

Physica A: Statistical Mechanics and its Applications

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Section: Discussionmentioning

confidence: 99%

The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model

Zhao

Zhang

Yuan

2018

Physica A: Statistical Mechanics and its Applications

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“…Wang et al in article [31] have considered the CTL immune response in HIV stochastic model; therefore, a stochastic HIV model with latent infection and CTL immune response will be our future work. In addition, under the influence of environment, the stochastic perturbation is not always treated as a constant but a periodic behavior [41]; thus HIV latent infection model regarding periodic perturbation is also our research work in the future. …”

Section: Discussionmentioning

confidence: 99%

A Stochastic HIV Infection Model with Latent Infection and Antiretroviral Therapy

Liu

Wang

Liu

et al. 2018

Discrete Dynamics in Nature and Society

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Recent studies have demonstrated that the latent infection is a major obstacle to the viral elimination in HIV infection process. In this paper, we formulate a stochastic HIV infection model to include both latent infection and combination drug therapies. We derive that the model solution is unique and positive, and the solution is global. By constructing appropriate stochastic Lyapunov functions, the existence of an ergodic stationary distribution is obtained when the critical condition is greater than one. Furthermore, through rigorous analysis and deduction, the extinction of the virus is established under certain conditions. Numerical simulations are performed to show that small intensity of white noises can maintain the existence of a stationary distribution, while large intensity of white noises is beneficial to the extinction of the virus.

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“…Therefore, the variability and randomness of the environment are fed through to the state of the epidemic [13]. A more realistic way of modeling infectious diseases is stochastic differential equation (SDE) models in many cases [2,[11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage

Guo

Cai

Zhang

et al. 2018

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• A stochastic epidemic model with media coverage is developed.• The global dynamics of the deterministic model is shown.• The stochastic dynamics of the SDE model is given.• The existence of a unique stationary distribution of the SDE model is displayed. a b s t r a c tThis paper aims to study an SIS epidemic model with media coverage from a general deterministic model to a stochastic differential equation with environment fluctuation. Mathematically, we use the Markov semigroup theory to prove that the basic reproduction number R s 0 can be used to control the dynamics of stochastic system. Epidemiologically, we show that environment fluctuation can inhibit the occurrence of the disease, namely, in the case of disease persistence for the deterministic model, the disease still dies out with probability one for the stochastic model. So to a great extent the stochastic perturbation under media coverage affects the outbreak of the disease.

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Periodic behavior in a FIV model with seasonality as well as environment fluctuations

Cited by 57 publications

References 40 publications

The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model

The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model

A Stochastic HIV Infection Model with Latent Infection and Antiretroviral Therapy

Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage

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