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
