The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence

Zhao, Ding; Zhang, Tiansi; Yuan, Sanling

doi:10.1016/j.physa.2015.09.092

Cited by 35 publications

(11 citation statements)

References 15 publications

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“…(See [1][2][3][4][5][6][7][8][9][10][11][12][13]). In recent years many authors have proposed and investigated various types of stochastic epidemic dynamical models with such disturbances (see, for example, [13][14][15][16][17][18][19][20][21][22][23][24][25][26]). Particularly, we can see that the SIS (susceptible-infected-susceptible) type stochastic epidemic models are proposed and investigated in many articles, see for example [6,13,15,17-20,] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the nonlinear incidence rates are very important substances in modelling the dynamics of epidemic systems. In recent years, many authors have investigated various types of stochastic epidemic models with nonlinear incidence (see, for example, [9,[24][25][26]). A stochastic SIS epidemic model with nonlinear incidence βS (I) is proposed in [24], where the authors established the threshold criteria on the extinction and permanence in the mean in probability meaning.…”

Section: Introductionmentioning

confidence: 99%

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A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

Hu¹,

Li²,

Zeng³

et al. 2018

Filomat

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In this paper, the stochastic SIS epidemic model with vaccination under regime switching is further investigated. A new threshold R s 0 which is different from that given in [22] is established. A new technique to deal with the nonlinear incidence and vaccination for stochastic epidemic model under regime switching is proposed. When R s 0 > 0, the existence of a unique stationary distribution and the ergodic property are obtained by constructing a new stochastic Lyapunov function with Markov switching. The corresponding result which is acquired in [22] is improved and extended.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

Hu¹,

Li²,

Zeng³

et al. 2018

Filomat

View full text Add to dashboard Cite

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“…Recently, the stochastic differential equation models of infectious diseases [20][21][22][23][24][25] have been greatly developed, but the stochastic differential equation model of the virus dynamic model has just been developed. The classic threedimensional stochastic model is studied in the earlier literatures [26][27][28][29], then the virus stochastic model with target T-cell logistic growth and CTL immune response is also developed in the last two years [30,31].…”

Section: Introductionmentioning

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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“…Mathematically, stochastic processes are usually used to describe the environmental noise. By using stochastic differential equations (SDE), several recent studies have taken into account the effects of environmental fluctuations in the study of infectious disease dynamics [2,3,11,20,32,30]. For instance, Chang et al [3] formulated a stochastic SIRS system with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis.…”

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confidence: 99%

“…They obtained thresholds for the persistence in mean and extinction of epidemic. By considering the role of the vaccine, Zhao et al [32] proposed a stochastic SIVS system and found that large environmental noise could suppress the outbreak of diseases. Keeping all the above work in mind, in this paper, we assume that environmental fluctuations are directly proportional to the population in model (1).…”

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confidence: 99%

Global analysis of a stochastic TB model with vaccination and treatment

Feng¹,

Qiu²

2019

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, a stochastic model is formulated to describe the transmission dynamics of tuberculosis. The model incorporates vaccination and treatment in the intervention strategies. Firstly, sufficient conditions for persistence in mean and extinction of tuberculosis are provided. In addition, sufficient conditions are obtained for the existence of stationary distribution and ergodicity. Moreover, numerical simulations are given to illustrate these analytical results. The theoretical and numerical results show that large environmental disturbances can suppress the spread of tuberculosis.2010 Mathematics Subject Classification. Primary: 92B05, 92D30; Secondary: 60H10. 2923 2924 TAO FENG AND ZHIPENG QIU compartmental model for TB. They also incorporated vaccination and treatment into the TB model. In this model the population is divided into five classes based on disease status, namely the uninfected individuals, the vaccinated individuals, the treated individuals, the infected individuals (individuals infected and shedding virus) and the recovered individuals (individuals previously infected with the virus but not currently shedding virus). At time t, the numbers in each of these classes are denoted by S(t), V (t), T (t), L(t) and I(t), respectively. The model also involves the following parameters:Λ the constant recruitment rate of the population, β the scaled transmission rate between S(t) and I(t), ρ 1 β the scaled transmission rate between S(t) and T (t), p the proportional coefficient of vaccinated susceptible S(t), u the per-capita natural mortality rate, α the disease-induced death rate of I(t), l the proportion coefficient from S(t) to L(t), δ the rate at which L(t) becomes I(t),ρ the rate at which T (t) becomes L(t), γ the rate at which I(t) becomes T (t).

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The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence

Cited by 35 publications

References 15 publications

A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

A Stochastic HIV Infection Model with Latent Infection and Antiretroviral Therapy

Global analysis of a stochastic TB model with vaccination and treatment

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