Please Solve in Maple

Solving a system of first-order ordinary differential equations

We will now consider a model that is a bit more realistic. We modify the equation to consider that people get immune to the disease. We add an additional function to represent the proportion of the population that is immune to the disease. This gives us a system of equations. Since the people that are immune do not contribute to the growth of the sick folks, the differential equation for is now

We also need a differential relation for the proportion of the population that is immune. The immune population increases as the sick population gets well and decreases with time, either because they die of old age, or from loss of immunity. The system of equations is

(The parameter is the Greek letter gamma and is Greek letter delta.) Notice that again we are only interested in values of and between 0 and 1, and also we are only interested in solutions with + at most 1.

Use Maple to do the following:

Compute the steady-states for this system symbolically (hint: do this simultaneously). Again, there are two cases, depending on whether ? is greater than or less than ?.

Using the following values for the symbolic constants, find the numeric steady-state solutions for and :

= 0.6, = 0.5, = 0.4, = 0.2

This system is too complicated for Maple to solve symbolically, so we will solve it numerically in MATLAB.