A mathematical eco-epidemiological model consisting of harvested prey–predator system involving fear and disease in the prey population is formulated and studied. The prey population is supposed to be separated into two groups: susceptible and infected. The susceptible prey grows logistically, whereas the infected prey cannot reproduce and instead competes for the environment’s carrying capacity. Furthermore, the disease is transferred through contact from infected to susceptible individuals, and there is no inherited transmission. The existence, positivity, and boundedness of the model’s solution are discussed. The local stability analysis is carried out. The persistence requirements are established. The global behavior of the system is investigated with the use of the Lyapunov method. An application to the Sotomoyar theorem of local bifurcation is performed around the equilibrium points. In the end, the system is numerically simulated to confirm our obtained analytical results and specify the control set of parameters. Bifurcation diagrams are used to show the dynamical behavior as a function of some parameters. It is obtained that the prey’s fear stabilizes the system, while the disease and harvest cause extinction in one or more species.
The first section of this research discussed the manner of the research from many sides like the problem it faces, importance of it , its targets ,boundaries, the way to collect and get information's and its assumption.
When the second chapter discussed the press – manufacturing and the development ,importance and types of newspapers, also its merits and weaknesses.
The third chapter talked about the scientific side and how to choose an assumption for the research . as it talked also about the apparent honest and stability tests that help in analyzing the research until getting results and so the right assumption for the research will be chosen.
And finally, the fourth chapter put highlight on the be
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