Stationary distribution and density function analysis of a stochastic epidemic HBV model

Ge, Junyan; Zuo, Wangmeng; Jiang, Daqing

doi:10.1016/j.matcom.2021.08.003

Cited by 25 publications

(11 citation statements)

References 20 publications

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“…By solving the Foker-Planck equation, Ge et al [9] given a specific expression of the probability density function of a stochastic HBV model near a unique local quasi-equilibrium, the theoretical results are verified by numerical simulation and are consistented with the HBV epidemic data in China.…”

Section: Introductionmentioning

confidence: 65%

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Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by Ornstein-Uhlenbeck process

Liang

Chang

2022

Preprint

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In this paper, we investigate a reaction-diffusion hepatitis B virus (HBV) infection model with mean-reverting Ornstein-Uhlenbeck process. For the model, the existence and uniqueness of the positive solution are proved, and the sufficient conditions is given of stationary distribution of solution. Finally, the existence of the stationary distribution is verified by numerical simulation, and the influence of noise intensity on disease was given. At the same time, it can also be observed that infected cells and viruses are susceptible to stochastic factors. Therefore, in order to better control the development of the disease, external interference of viruses and infected cells can be avoided or reduced as much as possible.

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Section: Introductionmentioning

confidence: 65%

“…Meanwhile, much work can be found on the dynamic behavior of HBV infection model [1][2][3][4][5][6][7][8][9][10]. For example, Din and Li [4] built stochastic HBV model with Markov switching and white noise, and verified the results of the theorem using runge Kutta method.…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by Ornstein-Uhlenbeck process

Liang

Chang

2022

Preprint

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“…A series of stochastic inequalities and strong number theorems were used to verify the results of hepatitis B extinction and persistence. Similar work had been done on stochastic epidemiological models of hepatitis B transmission with bilinear incidence [11–13]. In previous works [14–16], a stochastic epidemic model of hepatitis B transmission with standard incidence rates affected by environmental fluctuations was presented.…”

Section: Introductionmentioning

confidence: 91%

Dynamic modeling and analysis of acute and chronic hepatitis B epidemic with saturation incidence

Xue,

Fan,

2023

Math Methods in App Sciences

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The new stochastic and deterministic hepatitis B epidemic models are established. The models consist of four types: susceptible individuals, acutely infected hepatitis B individuals, chronically infected hepatitis B individuals and recovered individuals. This study focuses on the transmission dynamics of acute and chronic hepatitis B epidemics problems and the development of optimal control strategies to control the transmission of hepatitis B in the population. To this end, we first calculate the equilibrium point and basic reproduction number of the deterministic hepatitis B model to study the stability of the above model at the equilibrium point. Secondly, we give the basic reproduction number of the stochastic model of hepatitis B virus. A suitable Lyapunov function is constructed, and the solvability of the stochastic model is confirmed using the Itô formula. By using a series of stochastic inequalities and strong number theorems, the extinction and stationary distribution of hepatitis B in this stochastic model are obtained. Finally, the optimal control theory is used to develop an optimal control strategy for eliminating hepatitis B virus transmission. The Runge–Kutta method is used to simulate the above models to verify the rationality of our main theoretical results.

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“…Lemma 4.2 [22]. For the algebraic equation H 2 0 + C0 Θ 0 + Θ 0 CT 0 = 0, where H 0 = diag(1, 0, 0, 0), Θ 0 is a real symmetric matrix, and the standard matrix…”

Section: Existence Of Ergodic Stationary Distributionmentioning

confidence: 99%

Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus(COVID-19) with asymptomatic carriers

2022

Preprint

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In this paper, we propose a stochastic SEIR-type model to describe the propagation mechanism of coronavirus (COVID-19) in the population. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the stochastic model. Especially, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical simulations are introduced to validate the theoretical findings. spectively. S(t) denotes the number of individuals who are susceptible to the disease, E(t) represents the number of exposed (in the latent period) individuals and R(t) represents the number of individuals who have been infected and then removed from the possibility of being infected again at time t, respectively. All parameters are strictly positive and their descriptions are given in Table 1.

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Stationary distribution and density function analysis of a stochastic epidemic HBV model

Cited by 25 publications

References 20 publications

Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by Ornstein-Uhlenbeck process

Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by Ornstein-Uhlenbeck process

Dynamic modeling and analysis of acute and chronic hepatitis B epidemic with saturation incidence

Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus(COVID-19) with asymptomatic carriers

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