Controlling Biological Invasions: A Stochastic Host-Generalist Parasitoid Model

On a global scale, biological invasions are seriously destroying the stability of ecosystem, sharply decreasing biodiversity and even endangering human health and causing huge economic losses. However, there exist few effective measures controlling biological invasions. To more accurately examine the prevention and control effects of biological control on biological invasions in real environments of random fluctuations, we construct a stochastic host-generalist parasitoid model. We first establish, respectively, the sufficient conditions for the persistence and extinction of invasive hosts and generalist parasitoids, including (1) only the intrusive hosts go extinct; (2) only the generalist parasitoids are extinct, and (3) the intrusive hosts and generalist parasitoids are both extinct or persistent. Then, we perform a series of numerical simulations to verify the validity of the theoretical results obtained, based on which we further discuss the impacts of stochastic environmental fluctuations on the control of intrusive hosts, especially the possible changes of qualitative behavior caused by environmental noises in the bistable scenario. Our theoretical and numerical results indicate that compared with the invasive hosts, the generalist parasitoids are more vulnerable to environmental noises, and the prevention and control effects of biological control on invasive hosts are closely dependent to the initial population sizes. Thus, improving the ability of early detection of ecosystems, including the initial densities of biological populations and their dynamic characteristics, will provide effective predictive guidance for the prevention and control of alien host invasions.