Global stability of an SEIS epidemic model with recruitment and a varying total population size

Fan, Meng; Li, Michael Y.; Ke, Wang

doi:10.1016/s0025-5564(00)00067-5

Cited by 121 publications

(68 citation statements)

References 19 publications

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“…Assume that all parameters of (2) are positive constants. Using a similar argument as in [12], we can easily get the following results.…”

Section: Introductionmentioning

confidence: 71%

“…However, for some diseases, such as tuberculosis, schistosomiasis, measles, and AIDS, once a susceptible individual adequate contact with an infective, it becomes exposed, that is, infected but not infective. This individual remains in the exposed class for a certain latent period before becoming infective [10][11][12][13]. Particularly, Fan and Li in [12] established a class of SEIS epidemic model that incorporates constant recruitment, disease-caused death, and disease latency as follows: …”

Section: Introductionmentioning

confidence: 99%

“…where the meaning of the parameters can be found in the literature [12]. The author obtained that the global dynamics is completely determined by the basic reproduction number 0 = / ( + )( + + ).…”

Section: Introductionmentioning

confidence: 99%

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On a Stochastic SEIS Model with Treatment Rate of Latent Population

Gao

Dai

Zhang

et al. 2014

Abstract and Applied Analysis

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The asymptotic dynamics of a stochastic SEIS epidemic model with treatment rate of latent population is investigated. First, we show that the system provides a unique positive global solution starting from the positive initial value. Then, the long-term asymptotic behavior of the model is studied: if 0 , which is called the basic reproduction number of the corresponding deterministic model, is not more than unity, the solution of the model is oscillating around the disease-free equilibrium of the corresponding deterministic system, whereas if 0 is larger than unity, we show how the solution spirals around the endemic equilibrium of deterministic system under certain parametric restrictions. Finally, numerical simulations are carried out to support our theoretical findings.

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“…Assume that all parameters of (2) are positive constants. Using a similar argument as in [12], we can easily get the following results.…”

Section: Introductionmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On a Stochastic SEIS Model with Treatment Rate of Latent Population

Gao

Dai

Zhang

et al. 2014

Abstract and Applied Analysis

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“…Several investigators have focused on a single specific model, computing theoretical bifurcation points as well as some transient and steady-state solutions. This includes work on an SEI model (Pugliese, 1990), an SEIR model (Li, Graef, Wand and Karsai, 1999), and an SEIS model (Fan, Li and Wang, 2001). Models can be either closed or open.…”

Section: Introductionmentioning

confidence: 99%

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Enszer

Stadtherr

2010

Progress in Industrial Mathematics at ECMI 2008

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Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for the verified solution of nonlinear dynamic models we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method used is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.

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“…Several investigators have focused on a single specific model, computing theoretical bifurcation points as well as some transient and steady-state solutions. This includes work on an SEI model (Pugliese, 1990), an SEIR model (Li et al, 1999), and an SEIS model (Fan et al, 2001). Models can be either closed or open.…”

Section: Introductionmentioning

confidence: 99%

Verified Solution Method for Population Epidemiology Models with Uncertainty

Enszer¹,

Stadtherr²

2009

International Journal of Applied Mathematics and Computer Science

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Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.

show abstract

Global stability of an SEIS epidemic model with recruitment and a varying total population size

Cited by 121 publications

References 19 publications

On a Stochastic SEIS Model with Treatment Rate of Latent Population

On a Stochastic SEIS Model with Treatment Rate of Latent Population

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Verified Solution Method for Population Epidemiology Models with Uncertainty

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