Abstract
We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delayτpasses through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results.
Highlights
More attention has been paid to the eco-epidemiology model which considers both the ecological and epidemiological issues simultaneously due to the fact that most of the ecological populations suffer from various infectious diseases which have a significant role in regulating population sizes see, e.g., 1–6
Considering the time required by the susceptible individuals to become infective after their interaction with the infectious individuals, Zhou et al 8 formulated a delayed eco-epidemiology model and found that the Hopf bifurcation occurs when the delay passes through a sequence of critical values
We have incorporated the disease for the predator and the time delay into an eco-epidemiology model
Summary
More attention has been paid to the eco-epidemiology model which considers both the ecological and epidemiological issues simultaneously due to the fact that most of the ecological populations suffer from various infectious diseases which have a significant role in regulating population sizes see, e.g., 1–6. Considering the time required by the susceptible individuals to become infective after their interaction with the infectious individuals, Zhou et al 8 formulated a delayed eco-epidemiology model and found that the Hopf bifurcation occurs when the delay passes through a sequence of critical values They gave an estimation of the length of the time delay to preserve stability. Motivated by the works of Zhang et al 9 and Capasso and Serio 13 , in this paper, we are concerned with the effect of disease in predator and saturated incidence on the dynamics of eco-epidemiological model. To this end, we consider the following delay differential equations: xt rx t. The paper ends with a conclusion in the last section
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