diff --git a/inst/stan/functions/observation_model.stan b/inst/stan/functions/observation_model.stan
index 8c6fb594d..3c6f450f5 100644
--- a/inst/stan/functions/observation_model.stan
+++ b/inst/stan/functions/observation_model.stan
@@ -110,11 +110,15 @@ int[] report_rng(vector reports, real[] rep_phi, int model_type) {
   }
     
   for (s in 1:t) {
-    // defer to poisson if phi is large, to avoid overflow
-    if (sqrt_phi > 1e4) {
-      sampled_reports[s] = poisson_rng(reports[s] > 1e8 ? 1e8 : reports[s]);
+    if (reports[s] < 1e-8) {
+      sampled_reports[s] = 0;
     } else {
-      sampled_reports[s] = neg_binomial_2_rng(reports[s] > 1e8 ? 1e8 : reports[s], sqrt_phi);
+      // defer to poisson if phi is large, to avoid overflow
+      if (sqrt_phi > 1e4) {
+        sampled_reports[s] = poisson_rng(reports[s] > 1e8 ? 1e8 : reports[s]);
+      } else {
+        sampled_reports[s] = neg_binomial_2_rng(reports[s] > 1e8 ? 1e8 : reports[s], sqrt_phi);
+      }
     }
   }
   return(sampled_reports);