A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity

Fan, Kuangang; Zhang, Yan; Gao, Shujing; Xiang, Wei

doi:10.1016/j.physa.2017.04.055

Cited by 33 publications

(19 citation statements)

References 24 publications

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“…Various factors, such as vaccination, time delay, impulse and so on, are used to construct mathematical models and seek effective ways to eliminate infectious diseases. Time delay, which has great biologic meaning in epidemic systems, is often used [7][8][9][10]. Many scholars have also paid close attention to the effects of the temporary disease immunity of epidemic models, i.e., a fleeting immunity to a disease after recovery before becoming susceptible again.…”

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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“…Temporary immunity is another important phenomenon in the transmission of epidemic diseases, such as influenza, Chlamydia trachomatis, and Salmonella infection [12]. In the case of temporary immunity, an individual gets a fleeting immunity to a disease after recovery and then becomes susceptible again after some period.…”

Section: Introductionmentioning

confidence: 99%

A stochastic SIR epidemic model with Lévy jump and media coverage

2020

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A stochastic susceptible-infectious-recovered epidemic model with temporary immunity and media coverage is proposed. The effects of Lévy jumps on the dynamics of the model are considered. A unique global positive solution for the epidemic model is obtained. Sufficient conditions are derived to guarantee that the epidemic disease is extinct and persistent in the mean. The threshold behavior is discussed. Numerical simulations are given to verify our theoretical results.

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“…To model the spreading of diseases between different states, a spatial variable was added, which led to a partial differential system, see [5,6]. Already in 1975, Bailey discussed in [1] the relevance of stochastic terms in the mathematical model of epidemics, which is still an attractive way of modeling the uncertainty of the transmission and vaccines, see [7][8][9][10]. Although these modifications exist, so far there has been no success in generalizing the epidemic models to a general time scale to allow modeling a noncontinuous disease dynamics.…”

Section: Introductionmentioning

confidence: 99%

Exact solution to a dynamic SIR model

Böhner

Streipert

Torres

2019

Nonlinear Analysis: Hybrid Systems

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We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's approach. If the coefficients are constant, both solution methods yield the same result. After a brief introduction to time scales, we formulate the SIR (susceptible-infected-removed) model in the general time domain and derive its solution. In the discrete case, this provides the solution to a new discrete epidemic system, which exhibits the same behavior as the continuous model. The last part is dedicated to the analysis of the limiting behavior of susceptible, infected, and removed, which contains biological relevance. MSC 2010: 92D25; 34N05.

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A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity

Cited by 33 publications

References 24 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

A stochastic SIR epidemic model with Lévy jump and media coverage

Exact solution to a dynamic SIR model

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