System of three differential equations

Hello I can't solve this problem in Matlab. I have system of three differencial equations:

1) dS/dt= -r*S*I

2) dI/dt= r*S*I - a*i

3) dR/dt = a*I

where a and r are not time dependent and we are searching for their values. I have three vectors with the data for S, I and R. So i need to fint a and r.

Can someone tell me some code about this. I would be gratefull. Thank you !

[Sargondjani]

i actually know nothing about solving differential equations, but you might want to look at the 'ODE' solvers

[vasil enchev]

I looked at them first. There is something like:

syms x y(t)

but there is an error this syms x(t) is not recognizable.

[Walter Roberson]

Which MATLAB version are you using?

[vasil enchev]

well.. 7 and something I think

[Walter Roberson]

There have been a lot of changes over the "7" series, which dates back over 5 years. Could you be more specific? There have been notable changes in the symbolic toolbox.

[Walter Roberson]

There have been a lot of changes over the "7" series, which dates back over 5 years. Could you be more specific? There have been notable changes in the symbolic toolbox.

[vasil enchev]

It is 7.8.0... is it OK?

Answer 1

[Teja Muppirala]

So you have experimental data (S(t),I(t), and R(t)), and you are trying to find the parameters (a and r) that will make the ODE match your data, is that right? If so, I think this is the general idea : http://www.mathworks.co.jp/matlabcentral/answers/5054-solving-an-ode-with-best-fit-adjustment-to-empirical-observations

[vasil enchev]

Well no it isn't this I have a system of 3 equation and this is only for one...