Resumen de Analysis of the Predator–Prey Interactions: A Stochastic Model Incorporating Disease Invasion

Tao Feng, Xinzhu Meng, Tonghua Zhang, Zhipeng Qiu

• Environmental noise and infectious diseases are important factors affecting the development of the population. This paper develops a mathematical system to investigate the impacts of environmental noise and infectious diseases on predator–prey interactions. The globally unique positive solution is confirmed by using conventional methods. The stochastic uniform boundedness of the solution is obtained under certain conditions. Sufficient conditions for the persistence and extinction are given to measure the level of population size. Asymptotic dynamics of the solutions are carried out by two criteria parameters. The long-term dynamics of the solutions are demonstrated by numerical simulations. The results show that small-intensity environmental perturbations can cause population size to fluctuate around a certain level, while high-intensity environmental perturbations may lead to population extinction.