Permanence of a delayed SIR epidemic model with general nonlinear incidence rate

Jiang, Zhichao; Ma, Wanbiao

doi:10.1002/mma.3083

Cited by 8 publications

(3 citation statements)

References 24 publications

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“…In this paper, motivated by the above works and other studies, we propose the following dynamic system with general incidence function and delayed CTL immune response,

({, \begin{matrix} center \\ array \dot{x} (t) = λ - f (x (t), y (t)) y (t) - μ_{1} x (t), \\ array \dot{u} (t) = f (x (t), y (t)) y (t) + r y (t) - (σ + μ_{2}) u (t), \\ array \dot{y} (t) = σ u (t) - p y (t) z (t) - μ_{3} y (t), \\ array \dot{z} (t) = q y (t - τ) - μ_{4} z (t), \end{matrix})

where all parameters in system have the same biological meanings as in systems and . Figure illustrates all interactions described by system since the biological mechanism of systems and are the same.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics analysis of an HTLV‐1 infection model with mitotic division of actively infected cells and delayed CTL immune response

2018

Math Methods in App Sciences

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In this paper, we propose an improved human T‐cell leukemia virus type 1 infection model with mitotic division of actively infected cells and delayed cytotoxic T lymphocyte immune response. By constructing suitable Lyapunov functional and using LaSalle invariance principle, we investigate the global stability of the infection‐free equilibrium of the system. Our results show that the time delay can change stability behavior of the infection equilibrium and lead to the existence of Hopf bifurcations. Finally, numerical simulations are conducted to illustrate the applications of the main results.

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“…In this paper, motivated by the above works and other studies, we propose the following dynamic system with general incidence function and delayed CTL immune response,

({, \begin{matrix} center \\ array \dot{x} (t) = λ - f (x (t), y (t)) y (t) - μ_{1} x (t), \\ array \dot{u} (t) = f (x (t), y (t)) y (t) + r y (t) - (σ + μ_{2}) u (t), \\ array \dot{y} (t) = σ u (t) - p y (t) z (t) - μ_{3} y (t), \\ array \dot{z} (t) = q y (t - τ) - μ_{4} z (t), \end{matrix})

Section: Introductionmentioning

confidence: 99%

“…In this paper, motivated by the above works and other studies, [25][26][27][28][29][30][31][32] we propose the following dynamic system with general incidence function and delayed CTL immune response,…”

Section: Introductionmentioning

confidence: 99%

Dynamics analysis of an HTLV‐1 infection model with mitotic division of actively infected cells and delayed CTL immune response

2018

Math Methods in App Sciences

Self Cite

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“…In [16], the authors proposed a more general incidence rate which has a combination of monotonicity, nonmonotonicity and saturation properties as follows: Usually, there are two types of epidemic models: continuous-time models and discrete-time models. The continuous-time epidemic models described by differential equations have been widely investigated in many articles (for example, [10,11,21,25,30,31] and the references therein). In recent years, there has been an increasing interest in the study of discrete-time models (see [6,8,9,23,24,26,32] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Global analysis of a discrete sirs epidemic model with nonlinear incidence rate

Chaihao

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In this thesis, we prove some behaviors of a discrete SIRS epidemic model with a nonlinear incidence rate and a distributed time-delay. This model is constructed from the discretization of the corresponding continuous model by using a nonstandard finite difference method. The basic properties including the positivity and the boundedness of the solutions are established. We derive the existence of the disease-free equilibrium and the endemic equilibrium of the model. In addition, by applying Lyapunov function techniques, we prove that the disease-free equilibrium is globally attractive. Moreover, we give a sufficient condition for the permanence of the model. In order to illustrate our analytical results, finally, some numerical simulations are also included.

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Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function

Zhang

Meng

2019

Comp. Appl. Math.

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Permanence of a delayed SIR epidemic model with general nonlinear incidence rate

Cited by 8 publications

References 24 publications

Dynamics analysis of an HTLV‐1 infection model with mitotic division of actively infected cells and delayed CTL immune response

Dynamics analysis of an HTLV‐1 infection model with mitotic division of actively infected cells and delayed CTL immune response

Global analysis of a discrete sirs epidemic model with nonlinear incidence rate

Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function

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