santiagoyepes5

The SIR model is 3 EDO's

I am looking to estimate the parameters (b, y) with the method of Gauss Newton

The real data they give me are only the number of infected from day 1 to 14

The system lacks analytical solution

I solve with Euler this gives me the numerical approximation of the system,

Approach the problem of initial values ​​with Cauchy

(DS / dt) = -s * i * b

(DI / dt) = -s * i * b - y * i

(DR / dt) = y * i

Where

S: susceptible persons

I: Infected people

A: People removed

The problem is that when estimating the partial derivatives, I do not understand from which equation to estimate them since it seems logical that I can not do it from dI / dt since it represents the change of the infected with respect to the time osea the derivative thus I think Who should do it from its integral?

My problem is where I make my first partial derivatives and what are they to evaluate the initial matrix?

Any help, bibliographical, correctness, thank you.

regards

Santiago