MATLAB: 2-D plot with z-axis given in color - matlab

Question

My friends and I have been struggling to generate a 2-D plot in MATLAB with
$\eta_1$ and $\eta_2$ both varying in $0:0.01:1$ and the z-axis given by color.
We have a system of 8 differential equations, with HIVinf representing the total new HIV infections in a population over 1 year (HIVinf is obtained by integrating a function of $\eta_1, \eta_2$).
We are looping through $\eta_1$ and $\eta_2$ (two 'for' loops) with the ode45 solver within the 'for' loops.
Based on our prior numerical results, we should be getting much color variation in the 2D-plot. There should be patterns of darkness (high concentration of HIVinfections) along the edges of the plot, and lightness along the diagonals (low concentrations).
However, the following snippet does not produce what we want (I have attached the figure below).
[X,Y] = meshgrid(eta_11,eta_22);
figure;
pcolor(X,Y,AA);
shading interp;
I have attached the code below, as concisely as possible. The function ydot works fine (it is required to run ode45).
We would greatly appreciate if you could help us fix the snippet.
function All()
global Lambda mu mu_A mu_T beta tau eta_1 eta_2 lambda_T rho_1 rho_2 gamma
alpha = 20;
TIME = 365;
eta_11 = zeros(1,alpha);
eta_22 = zeros(1,alpha);
AA = zeros(1,alpha);
BB = zeros(1,alpha);
CC = zeros(1,alpha);
for n = 1:1:alpha
for m = 1:1:alpha
Lambda = 531062;
mu = 1/25550;
mu_A = 1/1460;
mu_T = 1/1825;
beta = 187/365000;
tau = 4/365;
lambda_T = 1/10;
rho_1 = 1/180;
rho_2 = 1/90;
gamma = 1/1000;
eta_1 = (n-1)./(alpha-1);
eta_11(m) = (m-1)./(alpha-1);
eta_2 = (m-1)./(alpha-1);
eta_22(m) = (m-1)./(alpha-1);
y0 = [191564208, 131533276, 2405629, 1805024, 1000000, 1000000, 500000, 500000];
[t,y] = ode45('SimplifiedEqns',[0:1:TIME],y0);
N = y(:,1)+y(:,2)+y(:,3)+y(:,4)+y(:,5)+y(;,6)+y(:,7)+y(:,8);
HIVinf1=[0:1:TIME];
HIVinf2=[beta.*(S+T).*(C1+C2)./N];
HIVinf=trapz(HIVinf1,HIVinf2);
AA(n,m) = HIVinf;
end
end
[X,Y] = meshgrid(eta_11,eta_22);
figure;
pcolor(X,Y,AA);
shading interp;
function ydot = SimplifiedEqns(t,y)
global Lambda mu mu_A mu_T beta tau eta_1 eta_2 lambda_T rho_1 rho_2 gamma
S = y(1);
T = y(2);
H = y(3);
C = y(4);
C1 = y(5);
C2 = y(6);
CM1 = y(7);
CM2 = y(8);
N = S + T + H + C + C1 + C2 + CM1 + CM2;
ydot = zeros(8,1);
ydot(1)=Lambda-mu.*S-beta.*(H+C+C1+C2).*(S./N)-tau.*(T+C).*(S./N);
ydot(2)=tau.*(T+C).*(S./N)-beta.*(H+C+C1+C2).*(T./N)-(mu+mu_T).*T;
ydot(3)=beta.*(H+C+C1+C2).*(S./N)-tau.*(T+C).*(H./N)-(mu+mu_A).*H;
ydot(4)=beta.*(H+C+C1+C2).*(T./N)+tau.*(T+C).*(H./N)- (mu+mu_A+mu_T+lambda_T).*C;
ydot(5)=lambda_T.*C-(mu+mu_A+rho_1+eta_1).*C1;
ydot(6)=rho_1.*C1-(mu+mu_A+rho_2+eta_2).*C2;
ydot(7)=eta_1.*C1-(mu+rho_1+gamma).*CM1;
ydot(8)=eta_2.*C2-(mu+rho_2+gamma.*(rho_1)./(rho_1+rho_2)).*CM2+(rho_1).*CM1;
end
end

Answer 1

Ok, I don't really know much about how the plot should look like, but your eta_11 and eta_22 are variables which are indexed only on the inner loop. That means that when n=1, m=1,2,3,...,alpha your eta_11/eta_22 will be a vector whose elements 1,2,3,...,alpha will be overwritten for every n. Since your meshgrid is outside of the loop, that could be a problem. Usually if you are plotting functions of two variables and you have said variables in 2 nested loops you just ignore the meshgrid. Like this
Option 1:
x=[0:0.01:1];
[x1,x2]=meshgrid(x,x);
y=x1+cos(x2);
contour(x,x,y,30);
Option 2
x=[0:0.01:1];
for i=1:101 %length(x)
for j=1:101
y(i,j)=x1(i)+cos(x2(j)); % It is important to index y with both
% loop variables
end
end
contour(x,x,y,30)