Dynamic Analysis of a Delayed Fractional-Order SIR Model with Saturated Incidence and Treatment Functions

In this paper, a delayed fractional-order SIR (susceptible, infected, and removed) epidemic model with saturated incidence and treatment functions is presented. Firstly, the non-negativity and boun...

[1]  Yongsheng Ding,et al.  A fractional-order differential equation model of HIV infection of CD4+ T-cells , 2009, Math. Comput. Model..

[2]  Wanbiao Ma,et al.  Permanence of an SIR epidemic model with distributed time delays , 2001 .

[3]  C. Vargas‐De‐León,et al.  Volterra-type Lyapunov functions for fractional-order epidemic systems , 2015 .

[4]  Xia Huang,et al.  A Numerical Method for Delayed Fractional-Order Differential Equations: Based on G-L Definition , 2013 .

[5]  Zhenhai Liu,et al.  Stability analysis for HIV infection of CD4+ T-cells by a fractional differential time-delay model with cure rate , 2014, Advances in Difference Equations.

[6]  E. Ahmed,et al.  On fractional order differential equations model for nonlocal epidemics , 2007, Physica A: Statistical Mechanics and its Applications.

[7]  Sompop Moonchai,et al.  Stability analysis of a fractional-order two-species facultative mutualism model with harvesting , 2017, Advances in Difference Equations.

[8]  Wenping Xiao,et al.  $$H_{\infty }$$H∞ filtering for discrete-time fuzzy stochastic neural networks with mixed time-delays , 2016 .

[9]  Yuxia Li,et al.  Global dissipativity and quasi-synchronization of asynchronous updating fractional-order memristor-based neural networks via interval matrix method , 2018, J. Frankl. Inst..

[10]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[11]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[12]  Shiwu Xiao,et al.  An SIRS model with a nonlinear incidence rate , 2007 .

[13]  Nemat Nyamoradi,et al.  Dynamic analysis of a fractional order prey–predator interaction with harvesting , 2013 .

[14]  Rui Xu,et al.  Global stability of a SIR epidemic model with nonlinear incidence rate and time delay , 2009 .

[15]  Rajivganthi Chinnathambi,et al.  Stability of fractional-order prey–predator system with time-delay and Monod–Haldane functional response , 2018 .

[16]  K. Rehan,et al.  HIV/AIDS epidemic fractional-order model , 2017 .

[17]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[18]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[19]  Davood Rostamy,et al.  Stability analysis of a fractional-order epidemics model with multiple equilibriums , 2016 .

[20]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[21]  Zhidong Teng,et al.  Backward bifurcation and global stability inan epidemic model with treatment and vaccination , 2014 .

[22]  Xianning Liu,et al.  Backward bifurcation of an epidemic model with saturated treatment function , 2008 .

[23]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[24]  Guillermo Fernández-Anaya,et al.  Lyapunov functions for a class of nonlinear systems using Caputo derivative , 2017, Commun. Nonlinear Sci. Numer. Simul..

[25]  D. Baleanu,et al.  Stability analysis of Caputo fractional-order nonlinear systems revisited , 2011, Nonlinear Dynamics.

[26]  Yasuhiro Takeuchi,et al.  Global stability of an SIR epidemic model with time delays , 1995, Journal of mathematical biology.

[27]  Rui Xu,et al.  Stability of a delayed SIRS epidemic model with a nonlinear incidence rate , 2009 .

[28]  Wendi Wang.  Backward bifurcation of an epidemic model with treatment. , 2006, Mathematical biosciences.

[29]  C. Connell McCluskey,et al.  Complete global stability for an SIR epidemic model with delay — Distributed or discrete , 2010 .

[30]  Jia Jia,et al.  Quasi-synchronisation of fractional-order memristor-based neural networks with parameter mismatches , 2017 .

[31]  C. Connell McCluskey.  Global stability for an SIR epidemic model with delay and nonlinear incidence , 2010 .

[32]  Zhen Wang,et al.  Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function , 2018, Nonlinear Dynamics.

[33]  Mei Song,et al.  Global stability of an SIR epidemicmodel with time delay , 2004, Appl. Math. Lett..

[34]  Ye Yan,et al.  Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay , 2012, Math. Comput. Simul..