# SIMbyom function call_deri.m (calculates the model output)

`Syntax: [Xout TE] = call_deri(t,par,X0v)`

This function calls the ODE solver to solve the system of differential equations specified in derivatives.m. As input, it gets:

• t the time vector
• par the parameter structure
• X0v a vector with initial states and one concentration (scenario number)

The output Xout provides a matrix with time in rows, and states in columns. This function calls derivatives.m.

## Start

```function [Xout TE] = call_deri(t,par,X0v)
```
```global glo   % allow for global parameters in structure glo
global zvd   % global structure for zero-variate data
```

## Initial settings

For the simulations, the regular options make little sense, so they have been removed. Keep useode=1 as this SIMbyom is not so useful for explicit functions.

```useode   = 1; % calculate model using ODE solver (1) or analytical solution (0)
eventson = 0; % events function on (1) or off (0)
stiff    = 0; % set to 1 to use a stiff solver instead of the standard one

% Unpack the vector X0v, which is X0mat for one scenario
X0 = X0v(2:end); % these are the intitial states for a scenario
```

## Calculations

This part calls the ODE solver to calculate the output (the value of the state variables over time). There is generally no need to modify this part. The solver ode45 generally works well. For stiff problems, the solver might become very slow; you can try ode15s instead.

```c  = X0v(1);     % the concentration (or scenario number)
t  = t(:);       % force t to be a row vector (needed when useode=0)

% specify options for the ODE solver
options = odeset; % start with default options
if eventson == 1
options = odeset(options, 'Events',@eventsfun); % add an events function
end
options = odeset(options, 'RelTol',1e-4,'AbsTol',1e-7); % specify tightened tolerances
% options = odeset(options,'InitialStep',max(t)/1000,'MaxStep',max(t)/100); % specify smaller stepsize

TE = 0; % dummy for time of events

if useode == 1 % use the ODE solver to calculate the solution
% call the ODE solver (use ode15s for stiff problems, escpecially for pulses)
if isempty(options.Events) % if no events function is specified ...
switch stiff
case 0
[~,Xout] = ode45(@derivatives,t,X0,options,par,c);
case 1
[~,Xout] = ode113(@derivatives,t,X0,options,par,c);
case 2
[~,Xout] = ode15s(@derivatives,t,X0,options,par,c);
end
else % with an events functions ... additional output arguments for events:
% TE catches the time of an event, YE the states at the event, and IE the number of the event
switch stiff
case 0
[~,Xout,TE,YE,IE] = ode45(@derivatives,t,X0,options,par,c);
case 1
[~,Xout,TE,YE,IE] = ode113(@derivatives,t,X0,options,par,c);
case 2
[~,Xout,TE,YE,IE] = ode15s(@derivatives,t,X0,options,par,c);
end
end
else % alternatively, use an explicit function provided in simplefun!
Xout = simplefun(t,X0,par,c);
end

if isempty(TE) || all(TE == 0) % if there is no event caught
TE = +inf; % return infinity
end
```

## Output mapping

Xout contains a row for each state variable. If you want to transform the model outputs, do it here.

```% % To obtain the output of the derivatives at each time point. For loop can
% % be removed if derivatives accepts vectors for the states. The values in
% % dXout might be used to replace values in Xout, if the data to be fitted
% % are the changes (rates) instead of the state variable itself).
% dXout = zeros(size(Xout)); % initialise with zeros
% for i = 1:length(t) % run through all time points
%     dXout(i,:) = derivatives(t(i),Xout(i,:),par,c);
%     % derivatives for each stage at each time
% end
```

## Events function

Modify this part of the code if eventson=1. This subfunction catches the 'events': in this case. This function should be adapted to the problem you are modelling (this one matches the byom_bioconc_... files, so it is of little use here). You can catch more events by making a vector out of values.

Note that the eventsfun has the same inputs, in the same sequence, as derivatives.m.

```function [value,isterminal,direction] = eventsfun(t,X,par,c)

Ct      = par.Ct(1); % threshold external concentration where degradation stops
nevents = 1;         % number of events that we try to catch

value       = zeros(nevents,1); % initialise with zeros
value(1)    = X(1) - Ct;        % thing to follow is external concentration (state 1) minus threshold
isterminal  = zeros(nevents,1); % do NOT stop the solver at an event
direction   = zeros(nevents,1); % catch ALL zero crossing when function is increasing or decreasing
```