Chapter 32
Nicholson–Bailey Host–Parasite Interaction
You knot of Mouth-Friends:..Most smiling, smooth, detested
Parasites.
(Shakespeare, Timon of Athens, 1607)
32.1 Nicholson–Bailey Host–Parasitoid Model
In Chap. 26 we modeled the spread of a parasitic infection in an insect population of
two life stages. The focus of that model was the spread of the infection. Therefore,
we did not pay any explicit attention to the fate of the parasitoid. In this chapter
however, we model explicitly the interactions between the host and the parasitoid
populations. Rather than setting up our model in terms of population sizes, we
specify host–parasitoid interactions in terms of population densities. What follows
here closely mirrors prior modeling by Ederstein-Keshet [1] and Brown and
Rothery [2].
In order to model the host–parasitoid interactions, we abstract away from the fact
that only specific lifecycle stages exhibit those interactions. After you worked
through this chapter, you may want to refine the model to account for the fact
that, for example, adult parasitoids lay their eggs in the pupae of hosts, but not in the
eggs of their hosts or with the larvae or adults.
Denote, respectively, H(t) and P(t) as the host and parasitoid densities in time
period t, and F(H(t), P(t)) as the fraction of hosts that is not parasitized. Then
H t þ 1
ð
Þ¼λ Ã H t
ð Þ Ã F H t
ð Þ, P t
ð Þ
ð
Þ
ð 32:1Þ
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_32,
© Springer International Publishing Switzerland 2014
267
Nicholson–Bailey Host–Parasite Interaction
You knot of Mouth-Friends:..Most smiling, smooth, detested
Parasites.
(Shakespeare, Timon of Athens, 1607)
32.1 Nicholson–Bailey Host–Parasitoid Model
In Chap. 26 we modeled the spread of a parasitic infection in an insect population of
two life stages. The focus of that model was the spread of the infection. Therefore,
we did not pay any explicit attention to the fate of the parasitoid. In this chapter
however, we model explicitly the interactions between the host and the parasitoid
populations. Rather than setting up our model in terms of population sizes, we
specify host–parasitoid interactions in terms of population densities. What follows
here closely mirrors prior modeling by Ederstein-Keshet [1] and Brown and
Rothery [2].
In order to model the host–parasitoid interactions, we abstract away from the fact
that only specific lifecycle stages exhibit those interactions. After you worked
through this chapter, you may want to refine the model to account for the fact
that, for example, adult parasitoids lay their eggs in the pupae of hosts, but not in the
eggs of their hosts or with the larvae or adults.
Denote, respectively, H(t) and P(t) as the host and parasitoid densities in time
period t, and F(H(t), P(t)) as the fraction of hosts that is not parasitized. Then
H t þ 1
ð
Þ¼λ Ã H t
ð Þ Ã F H t
ð Þ, P t
ð Þ
ð
Þ
ð 32:1Þ
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_32,
© Springer International Publishing Switzerland 2014
267