# How to graph the basic reproduction number R0 against two parameters on a 3D plot with planes?

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Amal Matrafi on 27 Nov 2023
Commented: Amal Matrafi on 27 Nov 2023
I need help with ploting the basic reproduction number, related to mathematical biology.
In fact, I tried drawing the basic reproduction number as figures in the paper, but I didn't get the same.
The paper containing the basic reproduction number (R0) and respective parameter values has been uploaded here, I hope you will help me in these drawing.
the code:
clear
clc
[X,Y] = meshgrid(0:0.01:0.5, 0:0.01:0.0381);
R0=6.2954e-04;
Z=R0*ones(size(X));
surf(X,Y,Z)
colormap('turbo')
xlabel('\mu')
ylabel('\Pi')
zlabel('R_0')
hold on
%Pi = 0.0381;
lambda=X;
d=0.00174;
beta1=0.00174;
beta2=0.00174;
a1=0.104;
a2=0.104;
wm=0.896;
d1=0.747;
d2=0.747;
gma1=0.253;
gma2=0.253;
theta=0.9;
%mu=0.1177;
mu=Y;
R1=lambda.*beta1./mu.*(a1+mu+wm);
R2=lambda.*beta2./mu.*(a2+mu+wm);
R0=max(R1,R2);
surf(X,Y,R0)
Amal Matrafi on 27 Nov 2023
Note: i named Pi here by lambda value.
Amal Matrafi on 27 Nov 2023
@Bora Eryilmaz I hope this post finds you well,
Can you help me with this problem please.

Bora Eryilmaz on 27 Nov 2023
The equations and plots in the article look inconsistent. For example, Eq. 3.21 seems to be missing a 1/mu term when they replace S0 = Pi/mu in the expressions.
[omega,mu] = meshgrid(0.1:0.01:0.5, 0.01:0.001:0.03);
beta1 = 0.00174;
beta2 = 0.00174;
a1 = 0.104;
a2 = 0.104;
Pi = 0.0381;
R1 = beta1*Pi./mu./(a1 + mu + omega); % Eqs. 3.21 and 3.22 seem to be missing the 1/mu factor.
R2 = beta2*Pi./mu./(a2 + mu + omega);
R0 = max(R1,R2);
s = surf(omega,mu,R0); % This looks consistent with the bottom right plot in Figure 2, except the vertical scale of R0.
xlabel('omega')
ylabel('mu');
zlabel('R0')
[Pi,mu] = meshgrid(0.1:0.01:0.5, 0.01:0.001:0.03);
R1 = beta1*Pi./mu./(a1 + mu + omega);
R2 = beta2*Pi./mu./(a2 + mu + omega);
R0 = max(R1,R2);
s = surf(Pi,mu,R0); % This looks consistent with the top right plot in Figure 2, except the vertical scale of R0.
xlabel('Pi')
ylabel('mu');
zlabel('R0')
Hope this helps.
Amal Matrafi on 27 Nov 2023
thank you so much for your response and help.

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