Algorithm for vitamin D concentration - problem with writting algorithm based on formulas - matlab

Question

I am trying to implement in Matlab an algorithm that calculates the vitamin D concentration in the blood based on some formulas from an article. Main formula is:
where:
- T is the day of the year for which the concentration is measured;
- A is constant for the simplest measurement described in the journal
- E (sun exposure on particular month in a year) is given in the article
- R (vitamin D concentration after single exposure for the sunlight) can be calculated using formula
where F, alpha, beta are constants, t - day.
An Author of the article wrote that after calculating concentration using C(t) formula he added a constant value 33 in every day.
Formula for R(t) is simple and my chart is the same as in the article, but I have a problem with formula for calculating C(t).
This is my code:
function [C] = calculateConcentration(A,E,T,R)
C=zeros(1,T);
C(1) = E(1)*A*R(1);
month=1;
for i=2:(T)
for j=1:i
if mod(j,30)==0 && month<12
month=month+1;
end
C(i) = C(i)+E(month)*A*R(T-j+1);
end
month=1;
end
for i=1:T
C(i)=C(i)+33;
end
end
Here is my chart:
Here is the chart from the article:
So, I have two problems with this chart. First, the biggest values on my chart are smaller than values on the chart from the article and second, my chart is constantly growing.
Thank you very much in advance help.
[EDIT] I attach the values of all constants and a function to calculate R (t).
function [R]= calculateR(T)
R = zeros(1,T);
F = 13;
alpha = 30;
beta = 3;
for i=1:T
R(i)=F*(2.^(-i/alpha)-2.^(-i/beta));
end
end
A=0.1;
T=365;
R = calculateR(T);
E = [0.03, 0.06, 0.16, 0.25, 0.36, 0.96, 0.87, 0.89, 0.58, 0.24, 0.08, 0.02];
plot(1:T,R)
C = calculateConcentration(A,E,T,R);
figure; plot(1:T,C);

Answer 1

Code formatting is horrible in comments so posting this as an answer.
I have stated what I think (!) is the basic problem with your code in the comments.
Cumulative sums can get confusing very quickly, hence it is often better to write them more explicitly.
I would write the function like so:
function C = calculateConcentration(T, E, A, R)
c = zeros(1, T);
% compute contribution of each individual day
for t = 1:T
c(t) = E(mod(floor(t / 30), 12) +1) * A * R(t);
end
% add offset
c(1) = c(1) + 33;
C = cumsum(c);
end
Disclaimer: I haven't written any matlab code in years, and don't have it installed on this machine, so make sure to test this.
EDIT
Not sure if the author is plotting what you say he is plotting.
If you chose A to be 100 (this might be fine with the correct choice of units), apply the offset of c(1) to all values of c (in my implementation), don't actually take the cumulative sum, but return (lowercase) c instead, and then only plot the data from the midpoint in each month, then you get the following plot:
However, it is worth noting that if you plot all data points you get the following.
At face value, I would say whoever came up with this model is full of BS. But a more definitive answer would require a careful read of the paper.