Dynamical Analysis Of Fractional-Order Eco-Epidemiological Models Incorporating Harvesting
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-epidemiolo...
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my-usm-ep.518482022-03-09T02:33:05Z Dynamical Analysis Of Fractional-Order Eco-Epidemiological Models Incorporating Harvesting 2021-03 Mohamed Al E, Elshahed Mahmoud Moustafa QA1 Mathematics (General) 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. 2021-03 Thesis http://eprints.usm.my/51848/ http://eprints.usm.my/51848/1/ELSHAHED%20MAHMOUD%20MOUSTAFA%20MOHAMED%20AL%20E.pdf application/pdf en public phd doctoral Perpustakaan Hamzah Sendut Pusat Pengajian Sains Matematik |
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Universiti Sains Malaysia |
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USM Institutional Repository |
| language |
English |
| topic |
QA1 Mathematics (General) |
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QA1 Mathematics (General) Mohamed Al E, Elshahed Mahmoud Moustafa Dynamical Analysis Of Fractional-Order Eco-Epidemiological Models Incorporating Harvesting |
| description |
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. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Mohamed Al E, Elshahed Mahmoud Moustafa |
| author_facet |
Mohamed Al E, Elshahed Mahmoud Moustafa |
| author_sort |
Mohamed Al E, Elshahed Mahmoud Moustafa |
| title |
Dynamical Analysis Of
Fractional-Order
Eco-Epidemiological Models
Incorporating Harvesting |
| title_short |
Dynamical Analysis Of
Fractional-Order
Eco-Epidemiological Models
Incorporating Harvesting |
| title_full |
Dynamical Analysis Of
Fractional-Order
Eco-Epidemiological Models
Incorporating Harvesting |
| title_fullStr |
Dynamical Analysis Of
Fractional-Order
Eco-Epidemiological Models
Incorporating Harvesting |
| title_full_unstemmed |
Dynamical Analysis Of
Fractional-Order
Eco-Epidemiological Models
Incorporating Harvesting |
| title_sort |
dynamical analysis of
fractional-order
eco-epidemiological models
incorporating harvesting |
| granting_institution |
Perpustakaan Hamzah Sendut |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2021 |
| url |
http://eprints.usm.my/51848/1/ELSHAHED%20MAHMOUD%20MOUSTAFA%20MOHAMED%20AL%20E.pdf |
| _version_ |
1747822106125533184 |