Bifurcation of an eco-epidemiological model with a nonlinear incidence rate

Dynamical behavior of a generalized eco-epidemiological system with prey refuge

“…Eco-epidemiological systems, which are applied to describe predator and prey interactions with diseases in one population or both populations, have become important tools in analyzing the spread and control of infectious diseases, and hence have received much attention since the Kermac-Mckendric SIR model was proposed [1][2][3][4][5][6][7][8][9][10]. In eco-epidemiology, researchers study an ecological system with disease either in prey or in predator or in both populations [10][11][12][13][14][15][16]. Anderson and May [1] proposed an animal (predator) and plant (prey) model with infectious diseases and investigated the invasion, persistence, and spread of diseases.…”

“…Bairagi et al [10] noticed the fact that the functional response plays an important role in determining the dynamical consequences of the population interactions, and hence conducted a comparative research on the stability aspects of a predator-prey system with a class of functional responses. Besides the published works mentioned above, more and more researchers have focused on the population interactions with diseases in prey or predator or both populations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

“…However, most of published research on eco-epidemiological systems incorporated a certain response function (e.g., Holling type functional response, Beddington-DeAngelis functional response) and a certain incidence rate (e.g., bilinear incidence, standard incidence, and saturation incidence), and investigated the dynamical behaviors of the considered systems [10,11,[14][15][16]. As far as we know, few works have focused on a model with a generalized functional response and obtained a generalized conclusion.…”

“…For the effect of prey refuge, the theoretical research and the field observations give a general conclusion that prey refuge can stabilize or destabilize the considered predation systems, and can prevent the prey extinction . Here, the stabilizing effect means that the interior equilibrium point changes from an unstable state to a stable state due to increase in the degree of prey refuge [16,21,26]. Otherwise, the destabilizing effect is observed [19,35].…”

“…Otherwise, the destabilizing effect is observed [19,35]. For examples, Gonzalez-Olivares and Ramos-Jiliberto [21], and Ruxton [16] proposed two continuous-time predator-prey systems with the assumption that a constant proportion of prey could move to refuges. Their studies found a stabilizing effect on the dynamical consequences of the considered systems.…”