Mohamed Al E, Elshahed Mahmoud Moustafa
(2021)
Dynamical Analysis Of
Fractional-Order
Eco-Epidemiological Models
Incorporating Harvesting.
PhD thesis, Perpustakaan Hamzah Sendut.
Abstract
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.
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