Asymptotic Behavior of a Stochastic Delayed Model for Chronic Hepatitis B Infection

Wu, Bo; Jia, Jianwen

doi:10.1155/2020/1875475

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…In previous works [14][15][16], a stochastic epidemic model of hepatitis B transmission with standard incidence rates affected by environmental fluctuations was presented. Wu et al [17] established a hepatitis B stochastic delay model with bilinear incidence. Using stochastic Lyapunov functional theory, the extinction and stable distribution of hepatitis B were studied.…”

Section: T)i(t) − (𝜇 0 + 𝜈) S(t)] Dt − 𝜂S(t)i(t)db(t)mentioning

confidence: 99%

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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Section: T)i(t) − (𝜇 0 + 𝜈) S(t)] Dt − 𝜂S(t)i(t)db(t)mentioning

confidence: 99%

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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Dynamic modeling and analysis of Hepatitis B epidemic with general incidence

Xue¹,

Zhang²,

Fan

2023

MBE

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<abstract><p>New stochastic and deterministic Hepatitis B epidemic models with general incidence are established to study the dynamics of Hepatitis B virus (HBV) epidemic transmission. Optimal control strategies are developed to control the spread of HBV in the population. In this regard, we first calculate the basic reproduction number and the equilibrium points of the deterministic Hepatitis B model. And then the local asymptotic stability at the equilibrium point is studied. Secondly, the basic reproduction number of the stochastic Hepatitis B model is calculated. Appropriate Lyapunov functions are constructed, and the unique global positive solution of the stochastic model is verified by Itô formula. By applying a series of stochastic inequalities and strong number theorems, the moment exponential stability, the extinction and persistence of HBV at the equilibrium point are obtained. Finally, using the optimal control theory, the optimal control strategy to eliminate the spread of HBV is developed. To reduce Hepatitis B infection rates and to promote vaccination rates, three control variables are used, for instance, isolation of patients, treatment of patients, and vaccine inoculation. For the purpose of verifying the rationality of our main theoretical conclusions, the Runge-Kutta method is applied to numerical simulation.</p></abstract>

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Asymptotic Behavior of a Stochastic Delayed Model for Chronic Hepatitis B Infection

Cited by 2 publications

References 31 publications

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

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

Dynamic modeling and analysis of Hepatitis B epidemic with general incidence

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