Abstract
A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.
Highlights
In recent years, many dynamical models characterizing the propagation of infectious disease [1–3], spread of computer viruses [4–6], and dynamics of some other systems [7–10] are studied by scholars
We propose a delayed ecoepidemic model by incorporating the time delay due to the gestation of the predator in the model studied in [31]
Compared with the work in [31], we mainly consider the effect of the time delay on the stability of system (2)
Summary
Many dynamical models characterizing the propagation of infectious disease [1–3], spread of computer viruses [4–6], and dynamics of some other systems [7–10] are studied by scholars. Ecoepidemiological research deals with the study of the spread of diseases among interacting populations, where the epidemic and demographic aspects are merged within one model They have been investigated by many scholars at home and abroad since the pioneer work of Kermack and McKendrick [11], and the interests in investigating the dynamics of ecoepidemic models will be increasing steadily due to its importance from both the mathematical and the ecological points of view. Upadhyay and Roy [13] proposed an ecoepidemic model with simple law of mass action and modified Holling type II functional response based on the model in [14]. They analyzed stability (linear and nonlinear) of the model.
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