DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

A DISCRETE-TIME HOST-PARASITOID MODEL
SOPHIA R.-J. JANG AND JUI-LING YU
We study a discrete-time host-parasitoid model proposed by May et al. In this model,
the parasitoid attacks the host first then followed by density dependence, where density
dependence depends only on those host populations that escaped from being parasitized.
Asymptotic dynamics of the resulting system are derived. There exist thresholds for which
both populations can coexist indefinitely.
Copyright © 2006 S. R.-J. Jang and J.-L. Yu. This is an open access article distributed under
the Creative Commons Attribution License, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
1. Introduction
It is well known that the sequence of density dependence and parasitism in the host life
cycle can have a significant effect on the population dynamics of the host-parasitoid interaction.
Consequently, the effect can have important implications for biological control. In
[10], May et al. proposed and numerically simulated three host-parasitoid models based
on the timing of parasitism and density dependence. In this work, we will study a model
proposed by May et al. [10] in which parasitism occurs first then followed by density dependence.
However, density dependence only depends on the remaining host population
that escaped being parasitized.
2. The model
Let N t be the host population at time t. The parasitoid population at time t is denoted
by P t . An individual parasitoid must find a host to deposit its eggs so that the parasitoid
can reproduce. It is assumed that parasitism occurs first then followed by density dependence.
Let β be the average number of offsprings that a parasitized host can reproduce
for a parasitoid individual. It is assumed that the number of encounters between host
and parasitoid populations at any time t ≥ 0 follows that of simple mass action, bN t P t ,
where the searching efficiency b is a constant. We assume that the number of encounters
is distributed randomly with a Poisson distribution. Consequently, the probability that
an individual host will escape from being parasitized when the parasitoid population is
Hindawi Publishing Corporation
Proceedings of the Conference on Differential & Difference Equations and Applications, pp. 451–455