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