# How can I store values in empty matrix to plot later?

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James Metz on 26 Nov 2020
Commented: Alan Stevens on 26 Nov 2020
I am trying to simulate an epidemic model based on the SIR model. I am having trouble with my code. My graphs are not showing up like i think they should. It is not an equation error. I think there may be a problem with the storage of my values or something. Please help.
%Epidemic Simulation
%Author: James Metz
%Date: Nov 15, 2020
%Define Natural Paramteres:
p = 0.0144; %Natural Birth Rate (Davidson County)
u = 0.008; %Natural Death Rate (Davidson County)
f = 0.03; %Infection Rate
r = 0.075; %Recovery Rate
m = 0.0001; %Death due to Infection Rate
v = 0.092; %Vaccination Rate
%Define Evaluation Time Paramteres:
dt = 1; %Time increments (days)
tEnd = 365; %Simulation length (days)
t = 1:dt:tEnd;
%Initialize Variables:
I = 10; %Initial infected population
R = 0; %Initial recovered population
S = 692587; %Initial susceptible population
I_1d = zeros(1, tEnd);
R_1d = zeros(1, tEnd);
S_1d = zeros(1, tEnd);
S_1d(1) = 692587;
I_1d(1) = 10;
R_1d(1) = 0;
%Loop through times:
for idx = 1:dt:tEnd-1
%Initialization:
S = S_1d(idx);
R = R_1d(idx);
I = I_1d(idx);
%Find changes in population numbers
dS_dt = -f*S*I - S*u - S*v + S*p; %Drop in unifected population
dI_dt = f*S*I - r*I - m*I - u*I; %Drop in infected population
dR_dt = r*I + S*v - u*R; %Gain in Recovered population
%Store new values:
S_1d(idx+1) = S_1d(idx) + dS_dt;
R_1d(idx+1) = R_1d(idx) + dR_dt;
I_1d(idx+1) = I_1d(idx) + dI_dt;
end
figure(1)
subplot(2,2,1)
plot(t, S_1d)
xlabel('Time (days)')
ylabel('Susceptible Population')
title('Drop in Susceptible Population due to Infection')
subplot(2,2,2)
plot(t, R_1d)
xlabel('Time (days)')
ylabel('Recovered Population')
title('Recovery Rate of Infected Persons')
subplot(2,2,3)
plot(t, I_1d)
xlabel('Time (days)')
ylabel('Infected Population')
title('Infection Rate of Susceptible Persons')
subplot(2, 2, 4)
plot(t, S_1d, 'green')
plot(t, R_1d, 'Blue')
plot(t, I_1d, 'red')
This is how my graphs are turining out:

KSSV on 26 Nov 2020
Check the values......are you getting NaN's after some point of the loop.
James Metz on 26 Nov 2020
Used isnan() function, but nothing yeilded a 'true'

Alan Stevens on 26 Nov 2020
You need to wotk with normalized population numbers. You can renormalize at the end.
%Epidemic Simulation
%Author: James Metz
%Date: Nov 15, 2020
%Define Natural Paramteres:
p = 0.0144; %Natural Birth Rate (Davidson County)
u = 0.008; %Natural Death Rate (Davidson County)
f = 0.03; %Infection Rate
r = 0.075; %Recovery Rate
m = 0.0001; %Death due to Infection Rate
v = 0.092; %Vaccination Rate
%Define Evaluation Time Paramteres:
dt = 1; %Time increments (days)
%tEnd = 365; %Simulation length (days)
tEnd =365;
t = 0:dt:tEnd;
elems = numel(t);
%Initialize Variables:
I0 = 10; %Initial infected population
R0 = 0; %Initial recovered population
S0 = 692587; %Initial susceptible population
I_1d = zeros(1, elems);
R_1d = zeros(1, elems);
S_1d = zeros(1, elems);
S_1d(1) = 1; % Normalize the numbers
I_1d(1) = I0/S0;
R_1d(1) = R0/S0;
%Loop through times:
for idx = 1:elems-1
%Initialization:
S = S_1d(idx);
R = R_1d(idx);
I = I_1d(idx);
%Find changes in population numbers
dS_dt = -f*S*I - S*u - S*v + S*p; %Drop in unifected population
dI_dt = f*S*I - r*I - m*I - u*I; %Drop in infected population
dR_dt = r*I + S*v - u*R; %Gain in Recovered population
%Store new values:
S_1d(idx+1) = S + dS_dt*dt;
R_1d(idx+1) = R + dR_dt*dt;
I_1d(idx+1) = I + dI_dt*dt;
end
S_1d = S_1d*S0; % Renormalize the numbers
R_1d = R_1d*S0;
I_1d = I_1d*S0;
figure(1)
subplot(2,2,1)
plot(t, S_1d)
xlabel('Time (days)')
ylabel('Susceptible Population')
title('Drop in Susceptible Population due to Infection')
subplot(2,2,2)
plot(t, R_1d)
xlabel('Time (days)')
ylabel('Recovered Population')
title('Recovery Rate of Infected Persons')
subplot(2,2,3)
plot(t, I_1d)
xlabel('Time (days)')
ylabel('Infected Population')
title('Infection Rate of Susceptible Persons')
subplot(2, 2, 4)
plot(t, S_1d, 'green')
plot(t, R_1d, 'Blue')
plot(t, I_1d, 'red')
This results in

Show 1 older comment
Alan Stevens on 26 Nov 2020
Normalizing the population numbers means dividing the values of S, I and R by the total number of people in the population. Then your equations work on fractions of the population. So a fraction of 1 means the whole population, a fraction of 0.9 means 90% of the population and so on.
James Metz on 26 Nov 2020
Oh that makes sense. If you don't mind me asking, why is it necessary in a code?
Alan Stevens on 26 Nov 2020
It wouldn't be necessary if your equations were linear, but terms like S*I make it so.

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