Resumen de Complex Dynamics in a Discrete Eco-Epidemiological Model with Fatal Disease in the Prey

Ceyu Lei, Xiaoling Han

• In this paper, we investigate the complex dynamics of a discrete-time predator–prey model with fatal disease in the prey. In theory, we obtain the preconditions for the existence of the equilibrium point and further derive sufficient conditions for the persistence and global stability of the coexistence equilibrium point. Additionally, we identify the existence of flip bifurcation and Neimark-Sacker bifurcation. Through numerical simulation, it is found that the dynamic behavior of the discrete model is extremely complex: (i) The increase in the birth rate of susceptible prey adversely affects the stability of the equilibrium point, but it promotes periodic behavior; (ii) Higher infection rates result in a decrease in the number of susceptible prey and predator; (iii) When the predation rate of the infected prey is high, the number of susceptible prey and predator increases, leading to the gradual disappearance of the infected prey.

  These findings may enrich the dynamic characteristics of the eco-epidemiological model.