TOPIC: Linear Algebra in MATLAB

Instructions. Record your solutions to Problems 1 and 2 below in separate function les. Record your solutions to the remaining problems in a single MATLAB le. Submit these les via the Blackboard link for Project 1. This project is very similar to the prisoner population problem presented in class. The notes from those lectures can be found on Blackboard under the lecture notes.

Background A new virus has been identied by doctors. There are three categories of people that we are interested in:

I - people currently immune to the virus S - people currently infected (S stands for sick) W - people not currently infected and not immune (W stands for well)

Death Rates Each day,

1% of the immune population dies. (-1% I)

4% of the sick population dies. (-4% S)

2% of the well population dies. (-2% W)

Birth Rates Each day,

3% of immune mothers give birth to immune children. (+3% I)

6% of well mothers give birth to well children. (+6% W)

Additional Information Each day,

8% of the well population gets infected and becomes sick (8% W S)

2% of the sick population recovers and becomes well (2% S W)

12% of the sick population recovers and becomes immune (12% S I)

3% of the immune population loses immunity due to old age and becomes well, but not immune (3% I W)

Problem 1. Write a function called PopAfterT that returns the population vector after t days. The input to the function should be four numbers: the number of days (t), the initial number of immune people (I0), the initial number of sick people (S0), and the initial number of well people (W0).

Problem 2. Write a function called PercPopAfterT that returns the population vector after t days expressed as percentages of that days total population. This function should take the same four inputs as the PopAfterT function from Problem 1.