Spatial Patterns of a Discrete Host-parasite Models with Allee Effects

In this paper, we introduce a diffusion term into the host-parasite model with the Allee effect to investigate the impact of population spatial diffusion on spatial pattern formation. Firstly, the local stability of the equilibrium points is discussed. Then, through numerical simulation, we found that under various diffusion parameters and initial conditions, the host and parasite populations exhibit point and strip patterns. The results show that the diffusion intensity and the initial population size are important factors in determining the spatial pattern of the population.