Answer to Question #163073 in Differential Equations for Ajay

Question

In a population of lions, the proportionate death rate is 0.55 per year and the

proportionate birth rate is 0.45 per year. Formulate a model of the population. Solve

the model and discuss its long term behavior. Also, find the equilibrium point of the

model.

Answer 1

Let B be the birth rate=0.45/year

and D be the death rate =0.55/year

Let N be the Population size of Model

Then Rate of propulation Growth

$\dfrac{dN}{dt}=\text {Birt rate-Death rate}=B-D$

$\dfrac{dN}{dt}=0.45-0.55=-0.1/year$

Different models depend on choices/observations/predictions of birth and death rates.

The equilibrium point of the Poulation size is found when the birth rate and death rate become equal.