Unraveling the transmission mechanism of animal disease: Insight from a stochastic eco-epidemiological model driven by Lévy jumps

In order to study the transmission mechanism of animal disease, thereby better controlling it and protecting human health, this work deals with a stochastic eco-epidemiological model, in which the infectious force of animal disease is described by the half-saturated incidence rate. And we attempt to introduce white noises and Lévy jumps as environmental perturbances in our proposed model. Before analyzing the dynamical characteristics of the stochastic model, the article firstly proves that there is a unique global positive solution. Then, we explore the thresholds to make the animal disease extinct from the perspective of environmental perturbances, which provide valuable suggestions for controlling the outbreak of animal disease. Furthermore, we analyze the long-term dynamical behavior of the stochastic model by establishing sufficient condition for the existence of a stationary distribution, which is of great significance for maintaining the ecological balance. Finally, we verify the theoretical results by numerical simulations and explore the impacts of white noises and Lévy jumps on the eco-epidemiological model, contributing to a better understanding of the stochastic model’s dynamical behaviors and the development of effective animal disease control strategies.