how to generate (multiple) realisations using Gillespie Algorithms

Hello, I would like to simulate this reaction

a->X

X-> X

at rates c. here is a code was written by Desmond Higham and I tried to adopted it to this reaction.

I would like to simulate different realisations . Could you please shed a light on this.

Your help is highly aprrecaited.

clf
clear all;
clc

rand('state',100)

%stoichiometric matrix
V = [1 -1];

%%%%%%%%%% Parameters and Initial Conditions %%%%%%%%%
nA = 6.023e23;             % Avagadro's number
vol = 1e-15;               % volume of system
X = zeros(1,1);
X(1) = 100; % molecules of substrate

c(1) = .4; c(2) =.1; c(3)=8; c(4)=.3;

t = 0;
tfinal = 100;

count = 1;
tvals(1) = 0;
Xvals(:,1) = X;


while t < tfinal
     a(1) = c(1);% calculate propensity functions
     a(2) = c(2)*X(1);
     asum = sum(a); 
     j = min(find(rand<cumsum(a/asum))); % select which reaction
     tau = log(1/rand)/asum; % select time
     X = X + V(:,j); %update X
    
     count = count + 1;
     t = t + tau; %Update time
     tvals(count) = t;
     Xvals(:,count) = X;
end

%%%%%%%%%%% Plots %%%%%%%%

L = length(tvals);
tnew = zeros(1,2*(L-1));
tnew(1:2:end-1) = tvals(2:end);
tnew(2:2:end) = tvals(2:end);
tnew = [tvals(1),tnew];
% 
Svals = Xvals(1,:);
ynew = zeros(1,2*L-1);
ynew(1:2:end) = Svals;
ynew(2:2:end-1) = Svals(1:end-1);
plot(tnew,ynew,'g-')
hold on

[yamen alharbi]

any help?

[Star Strider]

Relevant information on the Gillespie algorithm would be helpful. I didn’t find anything that related to it that had sufficient detail when I did an Interweb search several days ago. (Obviously, I have no prior experience with it.)

[yamen alharbi]

Thanks for your replay

Here are some links

The Gillespie started here and it has the algoriyhm in Figure 2.

https://pubs.acs.org/doi/pdf/10.1021/j100540a008

and here are some useful

https://jmahaffy.sdsu.edu/courses/f17/math636/beamer/stoc-04.pdf

https://epubs.siam.org/doi/pdf/10.1137/060666457

Thanks again

[Star Strider]

The only one that appears to be accessable is the SIAM paper. I’ll download it now and read it later. (The first is behind a paywall, the second offers only short descriptions and no links to other information.)

[yamen alharbi]

Thank you so much

Here is the first paper by Gillespie

https://www.caam.rice.edu/~cox/gillespie.pdf

and I have uploaded a copy of the same paper

Many Thanks again