How might an understanding of interconnected ecosystems help health officials determine how much money to allocate for the treatment of Lyme...

Let's begin with a general definition of ecosystem.  An ecosystem consists of all the living things sharing one habitat.  Because multiple species share the habitat, they also must either compete for resources or share them.  Thus they are interconnected.

Interconnection simply means that the organisms affect each other.  This effect can be either positive or negative.  In the case of Lyme disease, a bacteria carried by ticks will invade species on which the tick is a parasite.

Understanding the connection between bacteria, ticks, and the infected organisms, health officials can determine the most cost effective way to treat the disease.  For example, treating the symptoms of Lyme disease will fix the problem for an individual, but will not eradicate the disease.  Nor would it help to kill infected deer since they do not spread the disease.  However, killing the ticks that spread the disease or finding an anti-biotic to kill the bacteria would stop the spread.  The health official would then have to weigh the costs of methods used to kill the bacteria versus the cost of killing the ticks.