Dynamical Analysis Of Fractional-Order Eco-Epidemiological Models Incorporating Harvesting

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dc.contributor.authorMohamed Al E, Elshahed Mahmoud Moustafa
dc.date.accessioned2022-03-09T02:20:28Z
dc.date.available2022-03-09T02:20:28Z
dc.date.issued2021-03
dc.description.abstractIn 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.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/14829
dc.language.isoenen_US
dc.publisherUniversiti Sains Malaysiaen_US
dc.subjectMathematicsen_US
dc.titleDynamical Analysis Of Fractional-Order Eco-Epidemiological Models Incorporating Harvestingen_US
dc.typeThesisen_US
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