[R] Fwd: Using odesolve to produce non-negative solutions

[Jeremy Goldhaber-Fiebert]

Hi Spencer,

Thank you for your response. I also did not see anything on the lsoda help page which is the reason that I wrote to the list.

>From your response, I am not sure if I asked my question clearly.

I am modeling a group of people (in a variety of health states) moving through time (and getting infected with an infectious disease). This means that the count of the number of people in each state should be positive at all times. 

What appears to happen is that lsoda asks for a derivative at a given point in time t and then adjusts the state of the population. However, perhaps due to numerical instability, it occasionally lower the population count below 0 for one of the health states (perhaps because it's step size is too big or something). 

I have tried both the logarithm trick and also changing the relative and absolute tolerance inputs but I still get the problem for certain combinations of parameters and initial conditions. 

It occurs both under MS Windows XP Service Pack 2 and on a Linux cluster so I am pretty sure it is not platform specific.

My real question to the group is if there is not a work around in lsoda are there other ode solvers in R that will allow the constraint of solutions to the ODEs remain non-negative?

Best regards,
Jeremy
      

>>> Spencer Graves <spencer.graves at pdf.com> 6/8/2007 9:51 AM >>>
On the 'lsoda' help page, I did not see any option to force some 
or all parameters to be nonnegative. 

      Have you considered replacing the parameters that must be 
nonnegative with their logarithms?  This effective moves the 0 lower 
limit to (-Inf) and seems to have worked well for me in the past.  
Often, it can even make the log likelihood or sum of squares surface 
more elliptical, which means that the standard normal approximation for 
the sampling distribution of parameter estimates will likely be more 
accurate. 

      Hope this helps. 
      Spencer Graves
p.s.  Your example seems not to be self contained.  If I could have 
easily copied it from your email and run it myself, I might have been 
able to offer more useful suggestions. 

Jeremy Goldhaber-Fiebert wrote:
> Hello,
>
> I am using odesolve to simulate a group of people moving through time and transmitting infections to one another. 
>
> In Matlab, there is a NonNegative option which tells the Matlab solver to keep the vector elements of the ODE solution non-negative at all times. What is the right way to do this in R?
>
> Thanks,
> Jeremy
>
> P.S., Below is a simplified version of the code I use to try to do this, but I am not sure that it is theoretically right 
>
> dynmodel <- function(t,y,p) 
> { 
> ## Initialize parameter values
>
> 	birth <- p$mybirth(t)
> 	death <- p$mydeath(t)
> 	recover <- p$myrecover
> 	beta <- p$mybeta
> 	vaxeff <- p$myvaxeff
> 	vaccinated <- p$myvax(t)
>
> 	vax <- vaxeff*vaccinated/100
>
> ## If the state currently has negative quantities (shouldn't have), then reset to reasonable values for computing meaningful derivatives
>
> 	for (i in 1:length(y)) {
> 		if (y[i]<0) {
> 			y[i] <- 0
> 		}
> 	}
>
> 	S <- y[1]
> 	I <- y[2]
> 	R <- y[3]
> 	N <- y[4]
>
> 	shat <- (birth*(1-vax)) - (death*S) - (beta*S*I/N)
> 	ihat <- (beta*S*I/N) - (death*I) - (recover*I)
> 	rhat <- (birth*(vax)) + (recover*I) - (death*R)
>
> ## Do we overshoot into negative space, if so shrink derivative to bring state to 0 
> ## then rescale the components that take the derivative negative
>
> 	if (shat+S<0) {
> 		shat_old <- shat
> 		shat <- -1*S
> 		scaled_transmission <- (shat/shat_old)*(beta*S*I/N)
> 		ihat <- scaled_transmission - (death*I) - (recover*I)
> 		
> 	}	
> 	if (ihat+I<0) {
> 		ihat_old <- ihat
> 		ihat <- -1*I
> 		scaled_recovery <- (ihat/ihat_old)*(recover*I)
> 		rhat <- scaled_recovery +(birth*(vax)) - (death*R)
> 	
> 	}	
> 	if (rhat+R<0) {
> 		rhat <- -1*R
> 	}	
>
> 	nhat <- shat + ihat + rhat
>
> 	if (nhat+N<0) {
> 		nhat <- -1*N	
> 	}	
>
> ## return derivatives
>
> 	list(c(shat,ihat,rhat,nhat),c(0))
>
> }
>
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