A remark on stationary distribution of a stochastic SIR epidemic model with double saturated rates

Zhang, Yan; Fan, Kuangang; Gao, Shujing; Chen, Shihua

doi:10.1016/j.aml.2017.08.002

Cited by 33 publications

(18 citation statements)

References 9 publications

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“…Epidemic models are inevitably subject to environmental noise. Most epidemic models are driven by white noise, and many results have been achieved in this area [11][12][13][14][15][16][17][18][19]. However, under severe environmental perturbations, such as avian influenza, severe acute respiratory syndrome, volcanic eruptions, earthquakes, and hurricanes, the continuity of solutions may be broken; accordingly, a jump process should be introduced to prevent and control diseases [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

Fan

Zhang

Gao

et al. 2020

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tA stochastic susceptible-infectious-recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Lévy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system. Sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable Lyapunov functions. Based on the analysis, we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system.

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Section: Introductionmentioning

confidence: 99%

A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

Fan

Zhang

Gao

et al. 2020

Physica A: Statistical Mechanics and its Applications

Self Cite

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“…Remark 2: Recently, many scholars have investigated the synchronization and dissipativity of memristor-based neural networks (Chen et al, 2017, 2018; Li and Cao, 2018; Wang et al,. 2017; Zhang et al, 2018). For example, Chen et al (2018) investigated synchronization of coupled memristor-based neural networks with mixed delays and stochastic disturbance.…”

Section: Resultsmentioning

confidence: 99%

Periodically intermittent control for synchronized stationary distribution and synchronization of memristor-based stochastic coupled systems

Liu

Feng

et al. 2019

Transactions of the Institute of Measurement and Control

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This article is concerned with inner synchronized stationary distribution for memristor-based stochastic coupled systems for the first time. It is worth mentioning that periodically intermittent control that serves as a new technique is introduced into the investigation of synchronized stationary distribution. Based on the graph theory, the Lyapunov method and periodically intermittent control strategy, two main theorems that guarantee the existence of a synchronized stationary distribution are obtained, whose results illustrate that the existing region of synchronized stationary distribution depends on the control rate, coupled strength and so on. On the other hand, exponential synchronization is also taken into consideration and a theorem is presented. In addition, as applications, memristor-based stochastic coupled oscillators and stochastic coupled Chua’s circuits are presented to verify the practicability of theoretical results. Finally, two simulation examples are given to demonstrate the effectiveness and feasibility of theoretical results.

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“…Hence, the deterministic models have some limitations in predicting the future dynamics of the system accurately; stochastic models produce more valuable real benefits and can predict the future dynamics of the system accurately than deterministic models, and after one studies a deterministic model, extending the results to the stochastic case becomes a hot issue. To understand the impacts due to such randomness and fluctuations, stochastic differential equation (SDE) approach is widely used in many kinds of branches of applied science; many stochastic models have been proposed and studied, such as in the population ecology [11][12][13][14][15][16] and in the epidemiology [17][18][19][20][21][22][23][24][25][26][27], as well as in other fields [28][29][30]. Many valuable and interesting results were obtained.…”

Section: Introductionmentioning

confidence: 99%

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

Jia

2020

Complexity

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In this paper, a stochastic delayed model is constructed to describe chronic hepatitis B infection with HBV DNA-containing capsids. At first, the existence and uniqueness of the global positive solution are obtained. Secondly, the sufficient conditions are derived that the solution of the stochastic system fluctuates around the disease-free equilibrium E0 and the endemic equilibrium E∗. In the end, some numerical simulations are implemented to support our analytical results.

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A remark on stationary distribution of a stochastic SIR epidemic model with double saturated rates

Cited by 33 publications

References 9 publications

A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

Periodically intermittent control for synchronized stationary distribution and synchronization of memristor-based stochastic coupled systems

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

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