# [R] Using odesolve to produce non-negative solutions

From: Jeremy Goldhaber-Fiebert <JGOLDHAB_at_hsph.harvard.edu>
Date: Wed, 06 Jun 2007 12:17:31 -0400

Hello,

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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