# 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_my_first.m. As input, it gets:

`t`: the time point, provided by the ODE solver`X`: vector with the previous value of the states`par`: the parameter structure`c`: the external concentration (or scenario number)

Time `t` and scenario identifier `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: May 2017
- Web support: http://www.debtox.info/byom.html
- Back to getting started or byom_my_first.m

## Contents

## Start

The function statement, and make the global structure `glo` known here (not used in this function in this demo).

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

global glo % allow for global parameters in structure glo

## Unpack states

The state variables enter this function in the vector *X*. Here, we give them a more handy name (in this example, there is only one state).

```
Ci = X(1); % state 1 is the internal concentration at previous time point
```

## 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.

Kiw = par.Kiw(1); % bioconcentration factor, L/kg ke = par.ke(1); % elimination rate constant, d-1

## Calculate the derivatives

This is the actual model, specified as ODE.

if t>7 % for the depuration phase ... c = 0; % make the external concentration zero end dCi = ke * (Kiw * c - Ci); % first-order bioconcentration dX = [dCi]; % collect derivatives in vector dX to return to call_deri