[R] adaptivetau with time-dependent rate "parameters"; non-autonomous population dynamics via Monte Carlo

Rainer K. SACHS rainersachs at berkeley.edu
Mon Aug 25 06:01:37 CEST 2014

I am interested in "non-autonomous" population dynamics. The simplest
example is the deterministic ode of exponential growth or decay of a cell
population with average size s(t)>0:
ds/dt=M(t) s. Here M(t), instead of being constant, is an explicit function
of time and is independent of s, as can occur if the environment of s, e.g.
the temperature, changes in time due to external process independent of s.

Of course this equation, as well as some of its stochastic analogues, can
be solved explicitly, but more complicated stochastic models require Monte
Carlo approaches. I thought adaptivetau should work but it seems to balk at
such externally imposed time dependence. For example in the R-script
attached (an artificial example where one doesn't really need adaptivetau
because exact solutions happen to be available) k=0 gives an autonomous
problem and adaptivetau works, but for k=1 one gets time-dependent rates
per cell and adaptivetau appears to just use the initial parameter values
(corresponding to M(0) above) and give nonsense.

I read the package description and the vignettes by Johnson but didn't find
a solution. Is there a simple one?

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