# 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_guts1.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_guts.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.

S = X(1); % state 1 is the survival probability at previous time point Dw = X(2); % state 2 is the scaled damage 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.

kd = par.kd(1); % dominant rate constant, d-1 mw = par.mw(1); % median of threshold distribution, ug/L bw = par.bw(1); % killing rate, L/ug/d Fs = par.Fs(1); % fraction spread of threshold distribution (used in call_deri) hb = par.hb(1); % background hazard rate, d-1

## Calculate the derivatives

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

**Note:** scaled damage and background hazard are calculated here for every special case. However, survival is done here only for the pure SD model. Pure IT is calculated in call_deri.m.

dDw = kd * (c - Dw); % first order damage build-up from c (scaled) switch glo.sel case 1 % stochastic death h = bw * max(0,Dw-mw); % calculate the hazard rate dS = -(h + hb)* S; % change in survival probability (incl. background mort.) case 2 % individual tolerance dS = -hb* S; % only background hazard rate % mortality due to the chemical is included in call_deri! case 3 error('Use the GUTS models in the "full" or "reduced" folder for the IT+SD model!') end dX = [dS;dDw]; % collect both derivatives in one vector