# Interpreting intercept and beta coefficients from gamma hurdle model

I am using a gamma hurdle model based off of this earlier question and answer.

My response variable is a set of density estimates (20% are zeros and the rest are positive continuous values). I have never used a gamma model before and am unsure of how to interpret the intercept (beta0) and covariate coefficients (beta1). The relevant portion of my model (based off the above) is the gamma regression:

... # other parts of model

sd ~ dgamma(2, 2)

# for every observation
for(i in 1:nobs){

mu[i] <- pow(eta[i], -1)
eta[i] <- beta0[region[i]] + beta1[region[i]]*cov[i]

shape[i] <- pow(mu[i], 2) / pow(sd, 2)
rate[i] <- mu[i] / pow(sd, 2)

logGamma[i] <- log(dgamma(y[i], shape[i], rate[i]))

....} # other parts of model


I've googled for a couple of days but can't seem to figure out the useful search terms to address this. Any help or pointing in the direction of a resource would be very much appreciated.

EDIT:

I realized I should probably clarify what (I think) I do understand. 'beta0' and 'beta1' are the linear predictor to the object 'eta', which uses the inverse link function to become 'mu'. The gamma distribution is parameterized in JAGS with shape and rate. 'mu' is used in the calculation of these two parameters.

Is it accurate to say that 'beta0' is the mean that is used in the calculation of shape and rate, and 'beta1' is the covariate effect on that mean?