Global dynamics of an epidemic model with relapse and nonlinear incidence

2018 ◽  
Vol 42 (4) ◽  
pp. 1283-1291
Author(s):  
Yuming Chen ◽  
Jianquan Li ◽  
Shaofen Zou
Keyword(s):  
Epidemic Model ◽  
Global Dynamics ◽  
Nonlinear Incidence

scholarly journals Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates

2011 ◽  
Vol 39 (1-2) ◽  
pp. 15-34 ◽  
Author(s):  
Yoichi Enatsu ◽  
Eleonora Messina ◽  
Yukihiko Nakata ◽  
Yoshiaki Muroya ◽  
Elvira Russo ◽  
...  
Keyword(s):  
Wide Class ◽  
Epidemic Model ◽  
Incidence Rates ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Nonlinear Incidence Rates

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.

ANALYSIS ON AN EPIDEMIC MODEL WITH A RATIO-DEPENDENT NONLINEAR INCIDENCE RATE

2011 ◽  
Vol 04 (02) ◽  
pp. 227-239 ◽  
Author(s):  
BO LI ◽  
SANLING YUAN ◽  
WEIGUO ZHANG
Keyword(s):  
Qualitative Analysis ◽  
Incidence Rate ◽  
Computer Simulations ◽  
Epidemic Model ◽  
Mass Action ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Set Up ◽  
Disease Free

In this paper, we study the global dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectives to that of the susceptibles. The model has set up a challenging issue regarding its dynamics at the R-axis since it is not well defined on it. By carrying out a global qualitative 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.

scholarly journals Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Amine Bernoussi ◽  
Abdelilah Kaddar ◽  
Said Asserda
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Lasalle Theorem ◽  
Nonlinear Incidence Function ◽  
Disease Free

In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result.

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