# BYOM function derivatives.m (the model in ODEs)

Syntax: dX = derivatives(t,X,par,c)

This function calculates the derivatives for 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 point, provided by the ODE solver*X*is a vector with the previous value of the states*par*is the parameter structure*c*is the external concentration (or scenario number)

Time *t* and scenario name *c* are handed over as single numbers by call_deri.m (you do not have to use them in this function). Output *dX* (as vector) provides the differentials for each state at *t*.

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

## Contents

## Start

```
function dX = derivatives(t,X,par,c)
```

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

## Unpack states

The state variables enter this function in the vector *X*. Here, we give them a more handy name.

Cw = X(1); % state 1 is the external concentration Ci = X(2); % state 2 is the internal concentration

## 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 % % Optionally, include the threshold concentration as a global (see script) % Ct = glo.Ct; % threshold external concentration that stops degradation, mg/L

## Calculate the derivatives

This is the actual model, specified as a system of two ODEs:

if Cw > Ct % if we are above the critical internal concentration ... dCw = -kd * Cw; % let the external concentration degrade else % otherwise ... dCw = 0; % make the change in external concentration zero end dCi = ke * (Piw*Cw-Ci); % first order bioconcentration dX = [dCw;dCi]; % collect both derivatives in one vector dX