Database Reference
In-Depth Information
Chapter 11
Biological Control of Pestilence
Throughout this topic we have hinted at—or explicitly modeled—strategies that
interfere with the dynamics of pests and diseases, such as using repellents in the
malaria model or vaccination in the case of chicken pox. In this chapter, we focus
on such interferences and concentrate on biological methods to control pests. The
subsequent chapter then explores the effects of disease resistance.
11.1 Herbivory and Algae
11.1.1 Herbivore-Algae Predator-Prey Model
The first of our biological pestilence control models uses a simple predator-prey
model to show that even without migration, the system can exhibit a wide range of
responses. Assume that the prey are algae in a pond on which an herbivore grazes.
The data for this problem have been invented. (Normally, input data, parameters,
and initial conditions would be determined by experiment.)
The model consists of two main parts: one is for the change in the algae popula-
tion, and one is for the herbivore. The growth rate is a function of the algal density,
ALGAE. This function is monotonic and declining (Figure 11.1). Algal growth is
calculated as the product of the density and the growth rate.
The algae density is reduced through consumption by the herbivore. The con-
sumption per head is a nonlinear function of the algal density: the greater the den-
sity, the higher the consumption per head (Figure 11.2). The consumption rate is
simply the product of the number of herbivore and the consumption per head.
The herbivore death rate is determined by their average life span, which is a
nonlinear function of the consumption per head: the higher the consumption per
head, the longer the life span, within limits (Figure 11.3). Indirectly, the denser the
algae, the lower the herbivore death rate.
