Asymptotic dynamics of a deterministic and stochastic predator–prey model with disease in the prey species

In this paper, we discuss a predator–prey model with the Beddington–DeAngelis functional response of predators and a disease in the prey species. At first we study permanence and global stability of a positive equilibrium for the deterministic version of the model. Then we include a stochastic perturbation of the white noise type. We analyse the influence of this stochastic perturbation on the systems and prove that the positive equilibrium is also globally asymptotically stable in this case. The key point of our analysis is to choose appropriate Lyapunov functionals. We point out the differences between the deterministic and stochastic versions of the model. Copyright © 2013 John Wiley & Sons, Ltd.