POPULATION GROWTH

The population is ever increasing and determining its growth is as much important as trying to control it. The method described here can be used to determine the approximate popuation at any time in the future.

Population growth depends on two very important factors:

• Birth rate - The number of live births
• Mortality rate - The number of deaths

In real life population growth will depend on many factors. Also, these factors may vary with time. However, for the sake of simplicity of the problem, we have taken the two most important factors,and assumed them to be constant.

Let y(t) represent the size of the population at any time t. Let us assume that the population level is defined at t= 0 , i.e. y(0) =y where y is a constant. Let b >0 be the per capita average birth rate and m>0 be the per capita average mortality rate of the population. The assumptions that b , m are constants neglects many biological effects, but will be used for simplification of the problem. The population increases through births and decreases due to deaths:

rate of change of y = rate of births - rate of mortality

where rate of births is given by the product of per capita average birth rate b and size of the population y . Similarly, rate of mortality is taken as my

Let k=b-m , where k is net per capita growth rate of the population.

This mathematical model will help in estimating the population at any time T in the future. This will also help in estimating the requirement of resources for the future generation and the rate of depletion of resources, given that the rate of consumption of theses resources is a constant. This model will also help in calculating the per capita availability of food and other essential items

Summarizing the whole procedure we can come to the conclusion that the use of differential equations can be helpful even in determining the population at any time.

tex file

PDF

bib file