Abstract
A generalized eco-epidemiological system with prey refuge is proposed in this paper. The saturation incidence kinetics and a generalized functional response are used to describe the contact process and the predation process, respectively. Based on mathematical issue, the local and global stability properties, Hopf bifurcation, and permanence of the dynamical system are investigated. Based on the ecological aspects, the impact of prey refuge on the dynamical consequences of the eco-epidemiological system and the mechanism of prey refuge are discussed. The results reveal that the stabilizing and destabilizing effects occur under some certain conditions. Based on epidemiological issue, the controlling strategies of the infectious disease are proposed. The results show that the prey refuge can control the spread of disease by the relative level of prey refuge. This study has resolved some basic and interesting issues for an eco-epidemiological system with a generalized response function and the effect of prey refuge.
Highlights
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 have received much attention since the Kermac–Mckendric SIR model was proposed [1,2,3,4,5,6,7,8,9,10]
Saifuddin et al [13] explored an eco-epidemiological system with disease in the prey and weak Allee in predator, and considered the complex dynamics including stability properties and bifurcations
Based on ecological and epidemiological issues, our analyses reveal that the effect of prey refuge, the force of infection, and the converting efficiency of predators play an important role in the dynamical properties of the proposed system
Summary
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 have received much attention since the Kermac–Mckendric SIR model was proposed [1,2,3,4,5,6,7,8,9,10]. 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. In this paper we present a generalized eco-epidemiological system with the effect of prey refuge and the saturation incidence, and focus on the dynamical consequences of the proposed system and the explanations of the realistic meanings. Combining the generalized predation model (2.1) and the above assumptions, a generalized eco-epidemiological system with prey refuge and disease in prey is proposed by the following equations: S(t) = rS.
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