Spatial Structures in a Simple Model of Population Dynamics for Parasite-Host Interactions
Spatial patterning can be crucially important for understanding the behavior of interacting populations. Here we investigate a simple model of parasite and host populations in which parasites are random walkers that must come into contact with a host in order to reproduce. We focus on the spatial arrangement of parasites around a single host, and we derive using analytics and numerical simulations the necessary conditions placed on the parasite fecundity and lifetime for the population's long-term survival. We also show that the parasite population can be pushed to extinction by a large drift velocity, but, counterintuitively, a small drift velocity generally increases the parasite population.
Dong, JiaJia. "Spatial Structures in a Simple Model of Population Dynamics for Parasite-Host Interactions." Europhysics Letters 111, no. 4 (2015) : 48001.