Stability analysis of an SEIQV epidemic model with saturated incidence rate

Liu, Xingbo; Lijuan, Yang

doi:10.1016/j.nonrwa.2012.03.010

Cited by 109 publications

(51 citation statements)

References 33 publications

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“…For example, (a) the bilinear transmission rate biologically means that the more individuals get infected, the more susceptible individuals will become the infectives [7]. However, owing to the number of the susceptible individuals that contact with the infectives within a certain time is being limited, it is more reasonable to use the saturated incidence rate in modelling [8,9]; (b) in a general SIS epidemic model, there is only one epidemic disease, which is caused by one virus. In the real world, there might exist two epidemic diseases, one is caused by virus A, the other by virus B.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis

Meng

Zhao

Feng

et al. 2016

Journal of Mathematical Analysis and Applications

232

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Please cite this article in press as: X. Meng et al., Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis, J. Math. Anal. Appl. (2015), http://dx. AbstractIn this paper, we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis. Then we dedicate to develop a method to obtain the threshold of the stochastic SIS epidemic model. To this end, first, we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases. Second, we explore and obtain the threshold of a stochastic SIS system for the extinction and the permanence in mean of two epidemic diseases. The results show that a large stochastic disturbance can cause infectious diseases to go to extinction, in other words, the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance. This implies that the stochastic disturbance is conducive to epidemic diseases control. To illustrate the performance of the theoretical results, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis

Meng

Zhao

Feng

et al. 2016

Journal of Mathematical Analysis and Applications

232

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“…Here, we presume that    is the death rate due to disease without quarantine, 2  is the death rate due to disease after quarantine,  is the recovery rate after quarantine,  is the recovery rate without quarantine, 1 k , 2 k are quarantine rate of E , I respectively, 3 k is the recovery rate of E and  is the latent period of the epidemic. Because the variables R and Q do not appear in the first three equations in system (1), we further simplify system (1) and then obtain the following model…”

Section: Establishment Of the Modelmentioning

confidence: 99%

“…Because the variables R and Q do not appear in the first three equations in system (1), we further simplify system (1) and then obtain the following model…”

Section: Establishment Of the Modelmentioning

confidence: 99%

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Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

Li¹,

Xue²

2013

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In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any . Besides, the SEIQR model with nonlinear incidence rate is studied, and the 0  that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the 1 , k 3 k will effect changing trends of , S , E , I , Q R in system (1), which is obvious in simulations. Here, we take 3 k as an example to explain that.

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“…Therefore, many scholars have investigated epidemic models with vaccination (see e.g. [1,2,3,4,5,6,7]). Li and Ma [8] proposed the following SIS epidemic model with vaccination…”

Section: Introductionmentioning

confidence: 99%