Global stability of an SI epidemic model with feedback controls

Chen, Lijuan

doi:10.1016/j.aml.2013.09.009

Cited by 39 publications

(18 citation statements)

References 7 publications

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“…Lyapunov functions are often constructed to obtain the desired global asymptotical stability for the equilibria of the models. Recently, Chen and Sun [1] first deal with the stability of a homogeneous SI epidemic model by introducing feedback control variables-which capture the unpredictable disturbances and uncertain environments in realistic situations-although such control techniques have already been used in ecosystems [7,20]. Some optimal control strategies have also been studied in SIS models [16,17], which have implications in cyber security.…”

Section: Introductionmentioning

confidence: 99%

Global stability of disease-free equilibria in a two-group SI model with feedback control

Shang

2015

Nonlinear Analysis

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In this letter, a two-group SI epidemic model is tackled with an eye to population mobility. Using the method of Lyapunov functions, global stability of the disease-free equilibria with respect to one group as well as both groups is investigated. We find that the disease outbreak can be effectively controlled through adjusting the feedback control variables. Examples are worked out to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Global stability of disease-free equilibria in a two-group SI model with feedback control

Shang

2015

Nonlinear Analysis

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“…In addition, the single species with pure delay or distributed delay, the mutualism system, the epidemic model, the discrete Lotka-Volterra competitive system, and the cooperative system with feedback control were investigated in [5][6][7][8][9][10], and [11], respectively. Very recently, in [12] the author considered a logistic model with feedback of fractional order.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation in a single species logistic model with additive Allee effect and feedback control

Chen

2020

Adv Differ Equ

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In this paper, we propose a single species logistic model with feedback control and additive Allee effect in the growth of species. The basic aim of the paper is to discuss how the additive Allee effect and feedback control influence the above model's dynamical behaviors. Firstly, the existence and stability of equilibria are discussed under three different cases, i.e., weak Allee effect, strong Allee effect, and the critical case. Secondly, we prove the occurrence of saddle-node bifurcation and transcritical bifurcation with the help of Sotomayor's theorem. The above dynamical behaviors are richer and more complex than those in the traditional logistic model with feedback control. We find that both Allee effect and feedback control can increase the species' extinction property. We also reveal some new bifurcation phenomena which do not exist in the single-species model with feedback control (Fan and Wang in Nonlinear

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“…Dynamic mathematical models have provided a deeper understanding of the transmission process of infectious diseases [ 6 , 7 ]. There are many interesting results (see, e.g., [ 8 – 10 ]), which show that the simple susceptible-infective (SI) model can fit the transmission process of some diseases (measles, chicken pox, etc.) well.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Periodic Solution of a Susceptible-Infective Epidemic Model in a Polluted Environment under Environmental Fluctuation

Zhao

2018

Computational and Mathematical Methods in Medicine

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It is well known that the pollution and environmental fluctuations may seriously affect the outbreak of infectious diseases (e.g., measles). Therefore, understanding the association between the periodic outbreak of an infectious disease and noise and pollution still needs further development. Here we consider a stochastic susceptible-infective (SI) epidemic model in a polluted environment, which incorporates both environmental fluctuations as well as pollution. First, the existence of the global positive solution is discussed. Thereafter, the sufficient conditions for the nontrivial stochastic periodic solution and the boundary periodic solution of disease extinction are derived, respectively. Numerical simulation is also conducted in order to support the theoretical results. Our study shows that (i) large intensity noise may help the control of periodic outbreak of infectious disease; (ii) pollution may significantly affect the peak level of infective population and cause adverse health effects on the exposed population. These results can help increase the understanding of periodic outbreak patterns of infectious diseases.

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Global stability of an SI epidemic model with feedback controls

Cited by 39 publications

References 7 publications

Global stability of disease-free equilibria in a two-group SI model with feedback control

Global stability of disease-free equilibria in a two-group SI model with feedback control

Stability and bifurcation in a single species logistic model with additive Allee effect and feedback control

Stochastic Periodic Solution of a Susceptible-Infective Epidemic Model in a Polluted Environment under Environmental Fluctuation

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