The extinction and persistence of the stochastic hepatitis B epidemic model

Khan, Tahir; Khan, Amir; Zaman, Gul

doi:10.1016/j.chaos.2018.01.036

Cited by 81 publications

(53 citation statements)

References 22 publications

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“…ey showed that the booster vaccine of Hepatitis B is very necessary and useful. Khan et al [9] formulated the characteristics of HBV disease transmission and proposed the following deterministic Susceptible (S)-Infected (I)-Recovered (R) model: with initial data S(0) � S 0 > 0, I(0) � I 0 > 0, and R(0) � R 0 > 0. e positive parameters of the deterministic model (1) are given in the following list. e deterministic model constructed above can be improved by taking into account the unpredictable biological conditions [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Kiouach

Sabbar

2020

Computational and Mathematical Methods in Medicine

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Hepatitis B epidemic was and is still a rich subject that sparks the interest of epidemiological researchers. The dynamics of this epidemic is often modeled by a system with constant parameters. In reality, the parameters associated with the Hepatitis B model are not certain, but the interval in which it belongs to can readily be determined. Our paper focuses on an imprecise Hepatitis B model perturbed by Lévy noise due to unexpected environmental disturbances. This model has a global positive solution. Under an appropriate assumption, we prove the existence of a unique ergodic stationary distribution by using the mutually exclusive possibilities lemma demonstrated by Stettner in 1986. Our main effort is to establish an almost perfect condition for the existence of the stationary distribution. Numerical simulations are introduced to illustrate the analytical results.

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Section: Introductionmentioning

confidence: 99%

“…Khan et al [9] discussed the dynamics of a stochastic Hepatitis B epidemic model with varying population size. ey supposed that the effect of the random fluctuations is manifested as a perturbation in the Hepatitis B transmission rate.…”

Section: Introductionmentioning

confidence: 99%

Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Kiouach

Sabbar

2020

Computational and Mathematical Methods in Medicine

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“…Refs. [9][10][11][12][13][14][15][16][17][18]). But as far as we know, the studies on the dynamics of the stochastic SIRD model of Ebola seem to be rare.…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

Wang

Jia

2019

Adv Differ Equ

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In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii's theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results. MSC: Primary 37H10; 60H10; secondary 92C60; 92D30

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“…Many epidemic models have been discovered for the description of viral dynamic of hepatitis B, which are mostly using the deterministic approach (see for detail [5,9,11,18,23]). Recently Khan et al [10] presented a stochastic model for the transmission dynamic of hepatitis B.…”

Section: Introductionmentioning

confidence: 99%

“…In the resent study, we proposed a stochastic epidemic model with a varying population environment by extending the work of Khan et al [10]. Keeping in view the characteristic of hepatitis B, we divided the total population in four different compartments, the susceptible population in which the transmission rate is distributed by white noise, the infected individuals are further divided into two stages, namely the acute, the chronic hepatitis B individuals and the recovered population.…”

Section: Introductionmentioning

confidence: 99%

A stochastic model for the transmission dynamics of hepatitis B virus

Khan

Jung

Zaman

2019

Journal of Biological Dynamics

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In this paper, we formulate a stochastic model for hepatitis B virus transmission with the effect of fluctuation environment. We divide the total population into four different compartments, namely, the susceptible individuals in which the disease transmission rate is distributed by white noise, the acutely infected individuals in which the same perturbation occur, the chronically infected individuals and the recovered individuals. We use the stochastic Lyapunov function theory to construct a suitable stochastic Lyapunov function for the existence of positive solution. We also then establish the sufficient conditions for the hepatitis B extinction and the hepatitis B persistence. At the end numerical simulation is carried out by using the stochastic Runge-Kutta method to support our analytical findings.

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The extinction and persistence of the stochastic hepatitis B epidemic model

Cited by 81 publications

References 22 publications

Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

A stochastic model for the transmission dynamics of hepatitis B virus

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