Abstract
In this paper, we propose and investigate a nonlocal and time-delayed reaction–diffusion predator–prey model with disease spread in the prey which incorporates spatial heterogeneity and assimilation lag of consumed prey biomass into predator biomass. The SI-type subsystem of prey without predator is first studied, and we establish the threshold dynamics in terms of the basic reproduction number based on epidemiology. Then we show a series of sufficient conditions for the co-existence of prey and predator species, the global extinction of predator species and the global extinction of both the prey and predator species. Finally, a special example is explored via numerical simulations, where the influences of nonlocal effect, spatial heterogeneity and time delay on the invasion of the predator species are probed.
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