scholarly journals Coexistence of Limit Cycles and Homoclinic Loops in a SIRS Model with a Nonlinear Incidence Rate

2008 ◽  
Vol 69 (2) ◽  
pp. 621-639 ◽  
Author(s):  
Yilei Tang ◽  
Deqing Huang ◽  
Shigui Ruan ◽  
Weinian Zhang
Keyword(s):  
Incidence Rate ◽  
Limit Cycles ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Model

Global Dynamics of a Parasite-Host Model with Nonlinear Incidence Rate

2015 ◽  
Vol 25 (08) ◽  
pp. 1550102 ◽  
Author(s):  
Yilei Tang
Keyword(s):  
Incidence Rate ◽  
Global Attractor ◽  
Exponential Function ◽  
Limit Cycles ◽  
Hopf Bifurcations ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Dynamical Behaviors ◽  
Fractional Function

The paper is concerned with the effect of a nonlinear incidence rate Sp Iq on dynamical behaviors of a parasite-host model. It is shown that the global attractor of the parasite-host model is an equilibrium if q = 1, which is similar to that of the parasite-host model with a nonlinear incidence rate of the fractional function [Formula: see text]. However, when q is greater than one, more positive equilibria appear and limit cycles arise from Hopf bifurcations at the positive equilibria for the model with the incidence rate Sp Iq. It reveals that the nonlinear incidence rate of the exponential function Sp Iq for generic p and q can lead to more complicated and richer dynamics than the bilinear incidence rate or the fractional incidence rate for this model.

An SIRS model with a nonlinear incidence rate

2007 ◽  
Vol 34 (5) ◽  
pp. 1482-1497 ◽  
Author(s):  
Yu Jin ◽  
Wendi Wang ◽  
Shiwu Xiao
Keyword(s):  
Incidence Rate ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Model

Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate

2012 ◽  
Vol 479-481 ◽  
pp. 1495-1498 ◽  
Author(s):  
Jun Hong Li ◽  
Ning Cui ◽  
Hong Kai Sun
Keyword(s):  
Hopf Bifurcation ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Dulac Function ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Asymptotical Stable ◽  
Disease Free

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.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
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.

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

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.

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

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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