Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

[1]  Adem Kilicman,et al.  A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting , 2019, Mathematics.

[2]  A. A. Shaikh,et al.  Dynamics of an eco-epidemiological system with disease in competitive prey species , 2019, Journal of Applied Mathematics and Computing.

[3]  Jianwei Xia,et al.  Stability and bifurcation control of a delayed fractional-order eco-epidemiological model with incommensurate orders , 2019, J. Frankl. Inst..

[4]  I. M. Bulai,et al.  Eco-epidemiological interactions with predator interference and infection. , 2019, Theoretical population biology.

[5]  Dazhi Zhao,et al.  Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds , 2019, Appl. Math. Comput..

[6]  S. Mondal,et al.  Dynamics of a predator-prey model with nonlinear incidence rate, Crowley-Martin type functional response and disease in prey population , 2019, Ecological Genetics and Genomics.

[7]  Yuming Chen,et al.  Dynamical analysis of a stage-structured predator-prey model with cannibalism. , 2019, Mathematical biosciences.

[8]  Farah Aini Abdullah,et al.  Stage Structure and Refuge Effects in the Dynamical Analysis of a Fractional Order Rosenzweig-MacArthur Prey-Predator Model , 2019, Progress in Fractional Differentiation and Applications.

[9]  Lina Zhao,et al.  A priori and a posteriori error analysis of a staggered discontinuous Galerkin method for convection dominant diffusion equations , 2019, J. Comput. Appl. Math..

[10]  K. Balachandran,et al.  Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model , 2018, International Journal of Nonlinear Sciences and Numerical Simulation.

[11]  M. T. Monteiro,et al.  An epidemiological MSEIR model described by the Caputo fractional derivative , 2018, International Journal of Dynamics and Control.

[12]  N. Juneja,et al.  Conservation of a predator species in SIS prey-predator system using optimal taxation policy , 2018, Chaos, Solitons & Fractals.

[13]  Z. Teng,et al.  Stability analysis of a fractional-order predator–prey model incorporating a constant prey refuge and feedback control , 2018, Advances in Difference Equations.

[14]  Alakes Maiti,et al.  Stability analysis of a prey-predator fractional order model incorporating prey refuge , 2018, Ecological Genetics and Genomics.

[15]  Farah Aini Abdullah,et al.  Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge , 2018 .

[16]  Zhidong Teng,et al.  Global stability of an SI epidemic model with feedback controls in a patchy environment , 2018, Appl. Math. Comput..

[17]  Hai-Feng Huo,et al.  Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species , 2018, Journal of biological dynamics.

[18]  Masoud Shafiee,et al.  Dynamic analysis of fractional-order singular Holling type-II predator-prey system , 2017, Appl. Math. Comput..

[19]  K. Nugraheni,et al.  Dynamics of a Fractional Order Eco-Epidemiological Model , 2017 .

[20]  A. Lahiri,et al.  Analysis of a fractional order eco‐epidemiological model with prey infection and type 2 functional response , 2017, 1906.01226.

[21]  Subhas Khajanchi,et al.  Modeling the dynamics of stage-structure predator-prey system with Monod-Haldane type response function , 2017, Appl. Math. Comput..

[22]  Zhidong Teng,et al.  Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge , 2016, Journal of Applied Mathematics and Computing.

[23]  A. E. Matouk,et al.  Dynamical analysis, stabilization and discretization of a chaotic fractional-order GLV model , 2016 .

[24]  Benito M. Chen-Charpentier,et al.  Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order , 2016, Math. Comput. Simul..

[25]  Bashir Ahmad,et al.  Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system , 2015 .

[26]  Hongyong Zhao,et al.  The effect of vaccines on backward bifurcation in a fractional order HIV model , 2015 .

[27]  José Paulo Carvalho dos Santos,et al.  A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations , 2015 .

[28]  S. W. Schoombie,et al.  A proposed fractional-order Gompertz model and its application to tumour growth data. , 2015, Mathematical medicine and biology : a journal of the IMA.

[29]  Prashanta Kumar Mandal,et al.  Dynamics of a predator–prey model with disease in the predator , 2014 .

[30]  Benito M. Chen-Charpentier,et al.  A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1) , 2014 .

[31]  J. Nieto,et al.  On Fractional Derivatives and Primitives of Periodic Functions , 2014, 1405.6010.

[32]  Ranchao Wu,et al.  Hopf bifurcation analysis of a new commensurate fractional-order hyperchaotic system , 2014 .

[33]  S. Choi,et al.  Stability for Caputo Fractional Differential Systems , 2014 .

[34]  Yibin Kang,et al.  A predator–prey model with diseases in both prey and predator , 2013 .

[35]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[36]  Kai Diethelm,et al.  A fractional calculus based model for the simulation of an outbreak of dengue fever , 2013 .

[37]  Mohammed-Salah Abdelouahab,et al.  Hopf bifurcation and chaos in fractional-order modified hybrid optical system , 2012 .

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

[39]  S. Sivasundaram,et al.  Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions☆ , 2011, 1108.2825.

[40]  I. Petráš Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[41]  A. E. Matouk,et al.  Chaos, feedback control and synchronization of a fractional-order modified Autonomous Van der Pol–Duffing circuit , 2011 .

[42]  Debasis Mukherjee,et al.  Hopf bifurcation in an eco-epidemic model , 2010, Appl. Math. Comput..

[43]  Changpin Li,et al.  On the fractional Adams method , 2009, Comput. Math. Appl..

[44]  F. Hilker,et al.  Disease-induced stabilization of predator-prey oscillations. , 2008, Journal of theoretical biology.

[45]  Y. Hsieh,et al.  Predator–prey model with disease infection in both populations , 2008, Mathematical medicine and biology : a journal of the IMA.

[46]  David Greenhalgh,et al.  A predator–prey model with disease in the prey species only , 2007 .

[47]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[48]  I. Podlubny,et al.  Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives , 2005, math-ph/0512028.

[49]  Cosma Shalizi,et al.  Modeling Complex Systems , 2005 .

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

[51]  Zvia Agur,et al.  Theoretical examination of the pulse vaccination policy in the SIR epidemic model , 2000 .

[52]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

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

[54]  Kulbhushan Agnihotri,et al.  Global Stability of Harvested Prey–Predator Model with Infection in Predator Species , 2018 .

[55]  K. Hattaf,et al.  Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate , 2017 .

[56]  Lixia Yuan,et al.  STABILITY AND A NUMERICAL SOLUTION OF FRACTIONAL-ORDER BRUSSELATOR CHEMICAL REACTION SYSTEM , 2016 .

[57]  SANA P ANSARI,et al.  Stability analysis of fractional-order generalized chaotic susceptible–infected–recovered epidemic model and its synchronization using active control method , 2015 .

[58]  Cruz Vargas de León Volterra-type Lyapunov functions for fractional-order epidemic systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[59]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

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

[61]  Diana Stirling,et al.  Modeling Complex Systems , 2004 .