I am not sure how to use bernoulli_logit, I would like to fit a logistic regression model, but I am not sure is this model right?

infection ~ bernoulli_logit(b_0 + b_x* x[n]); // model

infection is the infection number, and my original formula is log(p/1-p) = b_0 + b_x* x, where p mean infection rate. So is this model right? because I cannot get the final result from this model, but there is no error comes out.