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

¹ Department of Physics & Astronomy, Bucknell University - Lewisburg, PA 17837, USA
² Materials Science Division, Argonne National Laboratory - Argonne, IL 60439, USA
³ Department of Mathematical Sciences, University of Wisconsin - Milwaukee, WI 53201, USA
⁴ Department of Physics & Astronomy, Iowa State University - Ames, IA 50011, USA
⁵ Department of Physics, Virginia Polytechnic Institute & State University - Blacksburg, VA 24061, USA
⁶ Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Str. 38, Dresden D-01187, Germany

^(a) jiajia.dong@bucknell.edu

Received: 14 June 2015
Accepted: 3 August 2015

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 populationÕs 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.