Abstract
A fractional-order eco-epidemiological model with disease in the prey population is formulated and analyzed. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the proposed fractional-order model. The existence, uniqueness, non-negativity and boundedness of the solutions are proved. The local and global asymptotic stability of all equilibrium points are investigated. Finally, numerical simulations are conducted to illustrate the analytical results. The occurrence of Hopf bifurcations and transcritical bifurcations for the fractional-order eco-epidemiological model are demonstrated. It is observed that the fractional order has a stabilization effect and it may help to control the coexistence between susceptible prey, infected prey and predator populations.
Highlights
The dynamics of the relationship between predators and their prey are topics of considerable interest in ecology and mathematical biology
Li et al [7] studied the global stability of an SI epidemic model with feedback controls in a patchy environment
The aim of this study is to proposed and analyzed a fractional-order ecoepidemiological model incorporating predator’s attack rate (α) and half saturation constant (a) with infection in prey population
Summary
The dynamics of the relationship between predators and their prey are topics of considerable interest in ecology and mathematical biology. Some studies have been carried out on eco-epidemiological models with disease either in prey [13,14,15,16] or in predator [17,18,19,20] or in both populations [21,22,23]. In [33, 34] a kind of fractional order eco-epidemiological model with disease in the prey population was proposed and some issues related to theoretical and numerical analyses were investigated. We consider the following fractional-order eco-epidemiological model incorporating a predator’s attack rate and half saturation constant: cDqS(t) rq βqSI d1 q γqI, cDqI(t) αqIP 1 + aI. The aim of this study is to proposed and analyzed a fractional-order ecoepidemiological model incorporating predator’s attack rate (α) and half saturation constant (a) with infection in prey population.
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