A fractional-Order Delay Differential Model for Ebola Infection and CD8+ T-cells Response: Stability analysis and Hopf bifurcation

In this paper, we study a fractional-order model with time-delay to describe the dynamics of Ebola virus infection with cytotoxic T-lymphocyte (CTL) response in vivo. The time-delay is introduced i...

[1]  Fathalla A. Rihan,et al.  Mathematical analysis of an SIS model with imperfect vaccination and backward bifurcation , 2014, Math. Comput. Simul..

[2]  Thomas Hoenen,et al.  Ebola virus: unravelling pathogenesis to combat a deadly disease. , 2006, Trends in molecular medicine.

[3]  Michael Y. Li,et al.  Global Dynamics of an In-host Viral Model with Intracellular Delay , 2010, Bulletin of mathematical biology.

[4]  Y. Chen,et al.  Fractional Processes and Fractional-Order Signal Processing , 2012 .

[5]  Zaid M. Odibat,et al.  Generalized Taylor's formula , 2007, Appl. Math. Comput..

[6]  Delfim F. M. Torres,et al.  Dynamics of Dengue epidemics when using optimal control , 2010, Math. Comput. Model..

[7]  Fathalla A. Rihan Computational methods for delay parabolic and time‐fractional partial differential equations , 2010 .

[8]  J. Audet,et al.  Immune evasion in ebolavirus infections. , 2015, Viral immunology.

[9]  J. Y. T. Mugisha,et al.  A host-vector model for malaria with infective immigrants , 2010 .

[10]  Fathalla A. Rihan Numerical Modeling of Fractional-Order Biological Systems , 2013 .

[11]  Zvi S. Roth,et al.  Mathematical Modeling of Ebola Virus Dynamics as a Step towards Rational Vaccine Design , 2010 .

[12]  Hanan Batarfi,et al.  On a fractional order Ebola epidemic model , 2015 .

[13]  Delfim F. M. Torres,et al.  Vaccination models and optimal control strategies to dengue. , 2013, Mathematical biosciences.

[14]  Thomas J. Anastasio,et al.  The fractional-order dynamics of brainstem vestibulo-oculomotor neurons , 1994, Biological Cybernetics.

[15]  Wei-Ching Chen,et al.  Nonlinear dynamics and chaos in a fractional-order financial system , 2008 .

[16]  Dumitru Baleanu,et al.  On Fractional SIRC Model withSalmonellaBacterial Infection , 2014 .

[17]  L. A. Rvachev,et al.  A mathematical model for the global spread of influenza , 1985 .

[18]  Wei Lin Global existence theory and chaos control of fractional differential equations , 2007 .

[19]  Fathalla A. Rihan,et al.  Delay differential model for tumour–immune dynamics with HIV infection of CD4+ T-cells , 2013, Int. J. Comput. Math..

[20]  M. Nowak,et al.  Population Dynamics of Immune Responses to Persistent Viruses , 1996, Science.

[21]  H. Tuckwell Viral Population Growth Models , 2005 .

[22]  K. Cole ELECTRIC CONDUCTANCE OF BIOLOGICAL SYSTEMS , 1933 .

[23]  José António Tenreiro Machado,et al.  Fractional model for malaria transmission under control strategies , 2013, Comput. Math. Appl..

[24]  A. Neumann,et al.  Global stability and periodic solution of the viral dynamics , 2007 .

[25]  Elif Demirci,et al.  A fractional order SEIR model with vertical transmission , 2011, Math. Comput. Model..

[26]  Tomonari Suzuki,et al.  A generalized Banach contraction principle that characterizes metric completeness , 2007 .

[27]  Ahmed M. A. El-Sayed,et al.  On the fractional-order logistic equation , 2007, Appl. Math. Lett..

[28]  Xianhua Tang,et al.  Stability and bifurcation analysis of a six-neuron BAM neural network model with discrete delays , 2011, Neurocomputing.

[29]  Jean M. Tchuenche,et al.  A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria , 2008, Appl. Math. Comput..