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.

scholarly journals The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Raid Kamel Naji ◽  
Arkan N. Mustafa
Keyword(s):  
Incidence Rate ◽  
Dynamical Behavior ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
Type Ii ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Dynamical Behaviors ◽  
Predator Model ◽  
Disease In Prey

This paper treats the dynamical behavior of eco-epidemiological model with nonlinear incidence rate. A Holling type II prey-predator model withSI-type of disease in prey has been proposed and analyzed. The existence, uniqueness, and boundedness of the solution of the system are studied. The local and global dynamical behaviors are investigated. The conditions, which guarantee the occurring of Hopf bifurcation of the system, are established. Finally, further investigations for the global dynamics of the proposed system are carried out with the help of numerical simulations.

GLOBAL DYNAMICS OF A MULTI-GROUP EPIDEMIC MODEL WITH GENERAL RELAPSE DISTRIBUTION AND NONLINEAR INCIDENCE RATE

2012 ◽  
Vol 20 (03) ◽  
pp. 235-258 ◽  
Author(s):  
JINLIANG WANG ◽  
JIAN ZU ◽  
XIANNING LIU ◽  
GANG HUANG ◽  
JIMIN ZHANG
Keyword(s):  
Incidence Rate ◽  
Host Population ◽  
Global Dynamics ◽  
Lyapunov Functionals ◽  
Nonlinear Incidence Rate ◽  
Oscillatory Solutions ◽  
Nonlinear Incidence ◽  
Persistence Theory ◽  
Graph Theoretical Approach ◽  
Derivatives Of

In this paper, we investigate a class of multi-group epidemic models allowing heterogeneity of the host population and that has taken into consideration with general relapse distribution and nonlinear incidence rate. We establish that the global dynamics are completely determined by the basic reproduction number R0. The proofs of the main results utilize the persistence theory in dynamical systems, Lyapunov functionals and a subtle grouping technique in estimating the derivatives of Lyapunov functionals guided by graph-theoretical approach. Biologically, the disease (with any initial inoculation) will persist in all groups of the population and will eventually settle at a constant level in each group. Furthermore, our results demonstrate that heterogeneity and nonlinear incidence rate do not alter the dynamical behaviors of the basic SIR model. On the other hand, the global dynamics exclude the existence of Hopf bifurcation leading to sustained oscillatory solutions.

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

scholarly journals Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Eric Ávila-Vales ◽  
Erika Rivero-Esquivel ◽  
Gerardo Emilio García-Almeida
Keyword(s):  
Numerical Simulations ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
General Incidence Rate ◽  
The Basic Reproduction Number

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form Sf(I), and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

scholarly journals Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Sanling Yuan ◽  
Bo Li
Keyword(s):  
Incidence Rate ◽  
Computer Simulations ◽  
Epidemic Model ◽  
Global Analysis ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Set Up ◽  
Disease Free

We study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics near the origin since it is not well defined there. By carrying out a global analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective individuals tends to zero as time evolves or the disease persists. Computer simulations are presented to illustrate the results.

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