Bifurcation of a predator–prey model with disease in the prey

Abstract

In this paper, a predator-prey model with disease in the prey is considered. Assume that the predator eats only the infected prey, and the incidence rate is nonlinear. We study the dynamics of the model in terms of local analysis of equilibria and bifurcation analysis of a boundary equilibrium and a positive equilibrium. We discuss the Bogdanov-Takens bifurcation near the boundary equilibrium and the Hopf bifurcation near the positive equilibrium; numerical simulation results are given to support the theoretical predictions.

Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response

“…It even causes the system to explode, which may be harmful to the ecological balance. Based on this point, a hybrid control strategy by combining the state feedback control and perturbation parameter is used in order to postpone the onset of an inherent bifurcation and enlarge the stable range in model (2).…”

“…In this part, we shall study the local stability of linearized system at the positive equilibrium and the existence of Hopf bifurcations for system (2).…”

“…Since the pioneering study of Anderson and May [1], great and interesting predatorprey models with disease were discussed by researchers recently [2][3][4][5][6][7][8][9][10][11]. In [2], Liu and Wang considered a predatorprey model with disease in the prey; the Bogdanov-Takens bifurcation and the Hopf bifurcation were analyzed. However, referring to diseases that are transmissible in different populations, Guo et al [12] studied an ecoepidemiological model with disease spreading within the predator population as follows:̇( …”

Dynamical transmission and effect of smoking in society

“…The nonlinearity and multi-scale behaviors in mathematical modeling describe the mutual relationship between parameters (Makinde, 2007). In last few decades, many biological models were studied in detail by using classical derivatives (Arafa et al, 2012;Kribs-Zaleta, 1999;Buonomo and Lacitignola, 2008;Liu and Wang, 2010;Haq et al, 2017).…”

Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control

“…Wang and Song [14] used mathematical model by infected pest to control the pest population. Hadeler and Freedman [15], Venturino [16,17], Kar and Mondal [18], Liu and Wang [19], Guo and Chen [20], Y. Zhang and Q. Zhang [21], Wang et al [22], and Wang and Chen [23] also worked on prey-predator model with the disease in the prey populations. In our present paper we consider two stages of infected pest, namely, infected pest in the first stage and infected pest in the last stage.…”