Periodic Solution and Ergodic Stationary Distribution of SEIS Dynamical Systems with Active and Latent Patients

Qi, Haokun; Leng, Xiaona; Meng, Xinzhu; Zhang, Tonghua

doi:10.1007/s12346-018-0289-9

Cited by 37 publications

(20 citation statements)

References 36 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

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“…If the epidemic models are conferred on temporary immunity, then we can establish SIS (susceptible, infections, susceptible) or SIRS (susceptible, infections, removed, susceptible) models. These models have been researched widely, from the deterministic to stochastic perspective [7][8][9][10][11][12][13][14][15][16]. However, the recovery of diseases may relapse, when latent infections reactivate and revert resulting in actively infected people.…”

Section: Introductionmentioning

confidence: 99%

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Liu

Meng

2020

Symmetry

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In this paper, a stochastic model with relapse and temporary immunity is formulated. The main purpose of this model is to investigate the stochastic properties. For two incidence rate terms, we apply the ideas of a symmetric method to obtain the results. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the extinction and persistence of this system. Then, we investigate the existence of a stationary distribution for this model by employing the theory of an integral Markov semigroup. Finally, the numerical examples are presented to illustrate the analytical findings.

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“…Furthermore, the theory and method of impulsive differential equations are widely used in many domains of biological science [17][18][19][20]. In reality, many populations are inevitably affected by stochastic disturbances [21][22][23][24][25][26][27][28], and many scholars have explored many stochastic dynamic systems and obtained some new results [29][30][31][32][33]. Recently, impulsive stochastic dynamics models attract the research interests of scholars [34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

Meng

2019

Discrete Dynamics in Nature and Society

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This paper proposes a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment. Using the theory of impulsive differential equations and Lyapunov functions method, we first investigate the dynamics of the stochastic system and establish the sufficient conditions for the extinction and the permanence of the microorganisms. Then we demonstrate that the stochastic periodic system has at least one nontrivial positive periodic solution. The results show that both impulsive toxicant input and stochastic noise have great effects on the survival and extinction of the microorganisms. Furthermore, a series of numerical simulations are presented to illustrate the performance of the theoretical results.

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Periodic Solution and Ergodic Stationary Distribution of SEIS Dynamical Systems with Active and Latent Patients

Cited by 37 publications

References 36 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

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

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