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

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Amal Matrafi am 27 Nov. 2023
Kommentiert: Amal Matrafi am 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')
shading interp
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)
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Amal Matrafi am 27 Nov. 2023
Note: i named Pi here by lambda value.
Amal Matrafi am 27 Nov. 2023
@Bora Eryilmaz I hope this post finds you well,
Can you help me with this problem please.

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### Akzeptierte Antwort

Bora Eryilmaz am 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.
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Amal Matrafi am 27 Nov. 2023
thank you so much for your response and help.

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