Dynamic analysis of disturbance propagation in ecological networks with quarantine items and proportional migration

Abstract

In order to study the stability of the ecosystem under external attack, we regard the ecosystem as a complex network and the species disturbance after the attack as an infectious disease. We establish an ecological network disturbance propagation model based on the infectious disease model, and analyze its dynamics with the above ideas. In this paper, the species are regarded as nodes in the network, and the predator–prey relationship is regarded as the edge of the network. When the ecosystem is attacked by external forces, the disturbance can be transmitted from a species to its predator or prey through the food chain, and the disturbed species can recover themselves and then return to a stable state. At the same time, we consider adding human quarantine and protection of disturbed species. In this way, all species in the ecosystem are divided into four states: undisturbed, disturbed, quarantine and recovered. By analyzing the dynamics of disturbance propagation, the critical threshold and equilibrium point of disturbance diffusion are determined, and the local and global stability of disease-free equilibrium and endemic equilibrium are analyzed. The results show that the existence of endemic equilibrium depends on the critical threshold of disturbance propagation, which is related to the structure of food web, the propagation proportion of disturbance and the recovery proportion of species after being attacked. The larger the propagation proportion is, the weaker the resistance stability is, and the easier the disturbance propagates in the system. The higher the recovery proportion of the disturbed species, the stronger the stability of the recovery rate, and the more difficult it is for the disturbance to propagate in the system. Then we regard human protection of species as species immunity, and choose the most effective species protection measures by comparing and analyzing the threshold changes under the three protection strategies. The results show that the moderately large neighbor nodes of the disturbed species should be protected. This kind of protection measure is the most effective and it is easier to restrain the propagation of disturbance. Finally, the food webs of 85 species in a pine forest in Otago, New Zealand is selected to analyze the propagation process of disturbance by numerical simulation.