Hello. Thank you. However this is used for Zero-Inflated Count Data. In my data, the number of days got the Min of 03 days. I think to apply this kind of model, I might think to shift my response: for example instead of days, using days-3... I will try but I think it might not help much.

Thank you for your answer again,

Another option might be to use a generalized Poisson distribution.  I know this can be done in STATA, but I don't know if/where one would do it in SAS.

Or, you could transform your data monotonically - say, via square root or log function.  This would be workable, since your minimum is >0 on the original scale.