Biology Reference
In-Depth Information
example of carnivory, where one meat-eating species hunts and feeds on
another animal, if the food organism is a plant, then the relationship is
described as herbivory. Parasitism and infectious disease also fall within the
definition of predation. In parasitism, one species benefits by living on or
inside the body of another. With infectious diseases, a pathogenic
microbe (a virus, bacterium, fungus, or protozoan) grows in or upon the
body of the host organism, causing varying levels of harm to the host,
ranging from annoyance (as with the common cold or athlete's foot) to
death (as with AIDS, cholera, or bubonic plague).
Regardless of the difference in specifics, several fundamental principles
are followed in the development of most models in which two or more
groups interact. In this chapter, our goal will be to understand those
principles as they apply to some of the classical epidemic and predator-
prey models and emphasize their biological meaning and mathematical
formulation.
I. INTRODUCTION TO INFECTIOUS DISEASE
A. Background
Throughout the centuries, more human lives have been lost to infectious
diseases than to wars. A well-documented example is the ''Spanish''
influenza pandemic of 1918-1919, which killed at least 25 million people
worldwide. Chillingly, a recent review of mortality figures by Johnson
and Mueller (2002) increases the conservative estimate to 50 million. In
contrast, deaths from World War I (which was then just ending) are
estimated at 8.5 million. Bubonic plague, cholera, rabies, yellow fever,
malaria, leprosy, and, most recently, AIDS, are humanity's lethal
enemies. Because the cause of such ailments was unknown for many
centuries, the fear of contagious diseases is rooted deeply in the human
mind. It is hard to fight an ''invisible enemy,'' and the fight against
infectious diseases has been slow, dangerous, and heroic.
That some diseases are infectious was recognized long ago, and it was also
known that the spread of such diseases could be restricted by isolating the
affected persons and places. For thousands of years, isolation was the only
effective tactic available in the fight with the invisible enemy.
Unfortunately, we are all familiar with the progression of an infectious
illness, from exposure through the miserable symptoms to resolution,
either by recovery or death. A mother wipes her infant's runny nose and
inadvertently rubs her own nose while on her way to the sink to wash
her hands. The viruses on her hand adhere to mucous membrane cells,
and a new infection is initiated.
In the beginning, the host does not realize that she is infected. Following
infection, the host enters a phase called the incubation period, during
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