Dynamical Analysis Of Fractional-Order Eco-Epidemiological Models Incorporating Harvesting
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Date
2021-03
Authors
Mohamed Al E, Elshahed Mahmoud Moustafa
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
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. It was found that the fractional-order, infectious disease and harvesting have a crucial effect on the dynamics
of the proposed fractional-order eco-epidemiological models. It was shown that introducing
harvesting to the proposed fractional-order eco-epidemiological models has a
stabilizing effect. It was observed that the fractional-order derivative may damp out oscillations
in the population and helps the stability of the proposed eco-epidemiological
models. It was also observed that the fractional-order derivative may play important
role in controlling chaotic dynamics and allow a sustained ecosystem where all species
survive. Furthermore, it was shown that the stability domain of the integer-order model
is smaller than the corresponding domain of the proposed fractional-order model.
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Keywords
Mathematics