Extinction and persistence of a stochastic SIRS model with nonlinear incidence rate and transfer from infectious to susceptible

An SIRS epidemic model with nonlinear incidence rate is studied. It is assumed that susceptible and infectious individuals have constant immigration rates. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the analytical results.

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Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment

The Scientific World JOURNAL ◽

10.1155/2013/209256 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 2

Author(s):

Junhong Li ◽

Ning Cui

Keyword(s):

Hopf Bifurcation ◽

Numerical Simulations ◽

Incidence Rate ◽

Dynamic Behavior ◽

Limit Cycle ◽

Nonlinear Incidence Rate ◽

Existence Of Equilibrium ◽

Nonlinear Incidence ◽

Sirs Model ◽

Asymptotical Stable

This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.

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Positive Recurrence and Extinction of Hybrid Stochastic SIRS Model with Nonlinear Incidence Rate

Journal of Mathematics ◽

10.1155/2021/6699024 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Liang Chen ◽

Shan Wang

Keyword(s):

Incidence Rate ◽

Dynamic Behavior ◽

Nonlinear Incidence Rate ◽

Positive Recurrence ◽

Nonlinear Incidence ◽

Sirs Model

In this paper, the dynamic behavior of a class of hybrid SIRS model with nonlinear incidence is studied. Firstly, we provide the condition under which the positive recurrence exists and then give the threshold R 0 S for disease extinction, that is, when R 0 S < 1 , the disease will die out. Finally, some examples are constructed to verify the conclusion.

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Pulse Vaccination Strategy in an SIVS Epidemic Model with General Nonlinear Incidence Rate

Advances in Analysis ◽

10.22606/aan.2016.12003 ◽

2016 ◽

Vol 1 (2) ◽

Cited By ~ 1

Author(s):

Dan Yu ◽

◽

Shujing Gao ◽

Youquan Luo ◽

Feiping Xie ◽

...

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Vaccination Strategy ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Pulse Vaccination

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Stability and Hopf bifurcation of a delayed epidemic model with stage structure and nonlinear incidence rate

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.2962 ◽

2013 ◽

Vol 37 (14) ◽

pp. 2150-2163

Author(s):

Rui Xu ◽

Xiaohong Tian

Keyword(s):

Hopf Bifurcation ◽

Incidence Rate ◽

Epidemic Model ◽

Stage Structure ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence

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Dynamical analysis of a reaction–diffusion SEI epidemic model with nonlinear incidence rate

International Journal of Biomathematics ◽

10.1142/s1793524521500418 ◽

2021 ◽

pp. 2150041

Author(s):

Jianpeng Wang ◽

Binxiang Dai

Keyword(s):

Steady State ◽

Incidence Rate ◽

Epidemic Model ◽

Reaction Diffusion ◽

Dynamical Analysis ◽

Asymptotically Stable ◽

Nonlinear Incidence Rate ◽

Globally Asymptotically Stable ◽

Nonlinear Incidence ◽

Positive Steady State

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] if [Formula: see text], the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if [Formula: see text]. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis.

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