Dynamical Analysis Of Fractional-Order Eco-Epidemiological Models Incorporating Harvesting - Mohamed Al E, Elshahed Mahmoud Moustafa (2021)
In this thesis, seven fractional-order eco-epidemiological models are formulated and analyzed: i) an eco-epidemiological model with infected prey incorporating harvesting; ii) an eco-epidemiological model with infected prey and logistic growth rate incorporating harvesting; iii) an eco-epidemiological model with infected prey and nonlinear incidence rate incorporating harvesting; iv) an eco-epidemiological model with infected predator and Holling type-II functional response incorporating harvesting; v) an eco-epidemiological model with infected predator and Holling type-IV functional response incorporating harvesting; vi) an eco-epidemiological model with two disease strains in the predator population incorporating harvesting; vii) a Hantavirus infection model incorporating harvesting. In order to clarify the characteristics of the proposed fractional-order eco-epidemiological models, existence, uniqueness, nonnegativity and boundedness of the solutions are analyzed. The local and global stability conditions of all biologically feasible equilibrium points of the proposed fractionalorder eco-epidemiological models are investigated by the Matignon’s condition and constructing suitable Lyapunov functions, respectively. The proof of the existence of transcritical bifurcation is given by using Sotomayor’s theorem. Numerical simulations are conducted to illustrate the analytical results. The proposed fractional-order ecoepidemiological models are shown to have rich dynamical behavior including bistability phenomena, supercritical Hopf bifurcation and transcritical bifurcation. The effects of fractional-order, infectious disease and harvesting on the stability of the proposed fractional-order eco-epidemiological models are investigated.