Spatial structures in a simple model of population dynamics for parasite-host interactions

TL;DR

This paper analyzes a simple spatial model of parasite-host interactions, revealing how parasite movement and drift influence population survival and spatial distribution.

Contribution

It provides analytical and numerical insights into how parasite fecundity, lifetime, and drift velocity affect long-term population survival in a spatial context.

Findings

Large drift velocity can cause parasite extinction.

Small drift velocity can increase parasite population.

Spatial arrangement depends on parasite fecundity and lifetime.

Abstract

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 populations 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.