# BYOM function simplefun.m (the model as explicit equations)

Syntax: Xout = simplefun(t,X0,par,c)

This function calculates the output of the model system. It is linked to the script files byom_bioconc_extra.m and byom_bioconc_start.m. As input, it gets:

*t*is the time vector*X0*is a vector with the initial values for states*par*is the parameter structure*c*is the external concentration (or scenario number)

Time *t* is handed over as a vector, and scenario name *c* as single number, by call_deri.m (you do not have to use them in this function). Output *Xout* (as matrix) provides the output for each state at each *t*.

- Author: Tjalling Jager
- Date: April 2017
- Web support: http://www.debtox.info/byom.html
- Back to index walkthrough_byom.html

## Contents

## Start

```
function Xout = simplefun(t,X0,par,c)
```

global glo % allow for global parameters in structure glo (handy for switches)

## Unpack initial states

The state variables enter this function in the vector _X_0.

Cw0 = X0(1); % state 1 is the external concentration at t=0 Ci0 = X0(2); % state 2 is the internal concentration at t=0

## Unpack parameters

The parameters enter this function in the structure *par*. The names in the structure are the same as those defined in the byom script file. The 1 between parentheses is needed as each parameter has 5 associated values.

kd = par.kd(1); % degradation rate constant, d-1 ke = par.ke(1); % elimination rate constant, d-1 Piw = par.Piw(1); % bioconcentration factor, L/kg Ct = par.Ct(1); % threshold external concentration that stops degradation, mg/L

## Calculate the model output

This is the actual model, specified as explicit function(s):

**Note:** this function is not completely identical to the solution of the system of ODE's. Here, I ignore the stop in degradation, which would require quite some fiddling around. Watch out that this solution is only valid when *ke* is NOT equal to *kd*!

Cw = Cw0 * exp(-kd*t); % concentration in water a = Cw0 * ke * Piw/(ke-kd); % this factor occurs twice in the solution Ci = a*exp(-kd*t) + (Ci0 - a) * exp(-ke*t); % internal concentration Xout = [Cw Ci]; % combine them into a matrix