%

clear all
close all

% TASK 1: Construct A with r = .5, print A (no semi-colon)
A = [0 3 0.1;0.5 0.6 0;0 0.3 0.4]; % CHANGE THIS
disp('The Matrix is:')
disp(A);

% TASK 2: Set x0, compute x7 and x30
x0 = [20 0 0]';
x7 = (A^7)*x0;
x30 = (A^30)*x0;
disp('The Population After 1 Week is:')
disp(x7');
disp('The Population After 1 Month is:')
disp(x30');

% Plot of the dominant eigenvalue as r varies
r = .5:.01:1; % values of r from .5 to 1
for i=1:length(r)
A(2,1) = 1-r(i);
lam = eig(A); % all eigenvalues
e(i) = max(lam); % dominant eigenvalue
end

figure
plot(r,e,'.-')
xlabel('Proportion of People Vaccinated (r)')
ylabel('Dominant Eigenvalue')

% TASK 3: Write a comment in the space below
%{
The zombie apocalypse will be avoided if at least 87% percentage of
people are vaccinated. This can be seen from the plot of dominat eigen
value vs the value of r. At 87% of vaccination, the dominant eigen value is
less than 1

%}

% TASK 4: Set r=r^*-.01, edit A, set lam1 as the dominant eigenvalue
r = 0.87-0.01; % CHANGE THIS
A = [0 3 0.1;1-r 0.6 0;0 0.3 0.4];
lam1 = max(eig(A)); % CHANGE THIS

% Plot the populations over time
if ~isnan(r)
D = 200;
x = [20; 0; 0

3.1 [Calculus and optimization For a given vector b â‚¬ Rd, Conside...