A mathematical model that was developed in the 1930s to describe the population dynamics among parasites (see parasitism) and their hosts, and predators and their prey. It can also be applied to the population dynamics of biological control. The model assumes that parasites and predators search randomly for hosts and prey, and it does not allow for stable parasite–host or predator–prey relationships. Consequently, the model produces unstable, oscillating populations and much subsequent work has aimed to stabilize it. The original model equations were: Nt+1=LNtexp(−aPt)Pt+1=Nt[1−exp(−aPt)]
where Nt is the number of hosts or prey at time t; Pt is the number of parasites or predators at time t; a is the area within which parasites or predators are searching; and L is the reproductive rate of the hosts or prey.
http://www.inhs.uiuc.edu/research/biocontrol/theoriesmodels/nbmodel.html. Describes the model and its application.
Subjects: Ecology and Conservation.