A stochastic predator-prey eco-epidemiological model with the fear effect

Dynamics of predator-prey systems is of great importance in ecosystems. In this paper, we present and analyse a stochastic eco-epidemiological predator-prey model where the influence of anti-predator behaviour is investigated due to the fear induced from the predators. Through mathematical analysis, it has been observed that the model has a unique and global positive solution. Sufficient criteria are established for the existence and ergodicity of a unique stationary distribution. Moreover, stochastic extinction for the whole eco-epidemiological system or only the infectious disease have been analysed.