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:

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.

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