scholarly journals STABILITY ANALYSIS OF A DELAYED FRACTIONAL ORDER SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE

2019 ◽  
Vol 32 (5) ◽  
Author(s):  
M. Naim ◽  
F. Lahmidi ◽  
A. Namir
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Fractional Order ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model

Backward Bifurcation in a Fractional-Order SIRS Epidemic Model with a Nonlinear Incidence Rate

2016 ◽  
Vol 17 (7-8) ◽  
pp. 401-412 ◽  
Author(s):  
A. M. Yousef ◽  
S. M. Salman
Keyword(s):  
Incidence Rate ◽  
Fractional Order ◽  
Epidemic Model ◽  
Local Stability ◽  
Host Population ◽  
Backward Bifurcation ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Disease Free

Abstract:In this work we study a fractional-order susceptible-infective-recovered-susceptible (SIRS) epidemic model with a nonlinear incidence rate. The incidence is assumed to be a convex function with respect to the infective class of a host population. Local and uniform stability analysis of the disease-free equilibrium is investigated. The conditions for the existence of endemic equilibria (EE) are given. Local stability of the EE is discussed. Conditions for the existence of Hopf bifurcation at the EE are given. Most importantly, conditions ensuring that the system exhibits backward bifurcation are provided. Numerical simulations are performed to verify the correctness of results obtained analytically.

scholarly journals Bifurcations of an SIRS epidemic model with nonlinear incidence rate

2011 ◽  
Vol 15 (1) ◽  
pp. 93-112 ◽  
Author(s):  
Zhixing Hu ◽  
◽  
Ping Bi ◽  
Wanbiao Ma ◽  
Shigui Ruan ◽  
...  
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model

scholarly journals A fractional order SIR epidemic model with nonlinear incidence rate

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Abderrahim Mouaouine ◽  
Adnane Boukhouima ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Incidence Rate ◽  
Fractional Order ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic

A fractional-order epidemic model with time-delay and nonlinear incidence rate

2019 ◽  
Vol 126 ◽  
pp. 97-105 ◽  
Author(s):  
F.A. Rihan ◽  
Q.M. Al-Mdallal ◽  
H.J. AlSakaji ◽  
A. Hashish
Keyword(s):  
Time Delay ◽  
Incidence Rate ◽  
Fractional Order ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence

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.

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