Introduction to Mathematical Models in Biology

In the past, mathematics has not been as successful a tool in the biological science as it has been in physical science. There are probably many reasons for this. Plan and animal are complex, made up of many components. The simplest of which man is just learning to comprehend. There seems to be mo fundamental biological law analogous to Newton's Law. thus the scientific community is a long way from understanding cause effect relationship in the biological world to the same degree that such law exist for spring mass system. In addition, many animal possess an ability to choose course of action, an ability that cannot be attribute to a spring mass system nor a pendulum.

In the following sections we will develop mathematical models describing one aspect of the biological world, the mutual relationship among plants, animals, and their environment, a field of study known as ecology. As a means of quantifying this science, the number of individuals of different species is investigated.

A DISCRETE ONE SPECIES MODEL

the rate of change of the population as measured over the time interval would be

this indicates the absolute rate of increase of the population. A quantity which will prove to be quite important is the rate of change of the population per Individual, R(t). This called the growth rate per unit time as measured ove the interval

source by Richard Haberman "Mathematical Model"
to be continue