\(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\W}[1]{ \; #1 \; }\)

user_trapezoidal.py

View page source

Using the Trapezoidal ODE Solver

Rates

The non-zero rates in this example are iota, rho, chi, and omega. They are all constant in age and time because they each have one smoothing grid point.

Integrands

The integrands for this example are prevalence, remission, mtexcess, and mtother. Modeling the prevalence integrand requires solving the ODE. The other integrands are direct measurements of the rates. To be specific, remission measures rho, mtexcess measures chi, and mtother measures omega.

Data

For each of the integrands there is one data point are age 50 and time 2000. No noise is added to the data but it is modeled as if it had a 10 percent coefficient of variation.

Random Effects

There are no random effects in this example.

rate_case

The rate case for this example is trapezoidal . This case has does not require any of the rates to be positive, so we use a lower limit of one for all the rates.