I need to set in R a template for the following data set:
t <- c(15.0169, 13.0286, 11.0257, 10.0172, 9.0087, 8.0157, 7.0230,
6.0300, 5.0229, 4.0158, 3.0231, 2.0302, 1.0221, 0.0000)
N <- c(7.9709, 7.9146, 7.9225, 7.8392, 7.7743, 7.2591, 6.6429,
6.1186, 5.4656, 4.8126, 4.1963, 3.6077, 3.4141, 3.4135)
P <- c(5.2141, 3.7615, 2.5382, 1.8807, 1.8433, 0.7492, 0.6312,
0, 0, 0, 0, 0, 0, 0)
The model consists of the equations:
dN / dt = mu / (1 + exp (-4 * (t - lambda))) * (1 - exp (N - Nmax))
dP / dt = alpha * N + beta * dN / dt
So there are five adjustable parameters: mu , lambda , Nmax , alfa and beta . I know the first ODE has an analytical solution, but I would like to adjust the system without solving this ODE analytically. Can anyone help me with the script?