Motivated by a real clinical dataset on the periodontal disease (PD), we develop a joint (shared parameter) model for the tooth-level current status (survival) response and the subject-level count response of available tooth-sites. We allow the time-to-event to follow the semiparametric generalized odds ratio (GOR) model with a cure fraction, while the count responses are allowed to follow a conditional Poisson regression model, and these two are connected through a shared random component. We develop an EM algorithm for parameter estimation. For statistical inference, we derive the asymptotic distribution of the estimator when a semiparametric approach is adopted to model the nonparametric component of the GOR model. We assess the operating charateristics of the proposed approach through simulation studies. Post model building, we illustrate our methodology through our motivating dataset by picking up the best model via the new diagnostic result using the AIC/BIC decomposition, and interpreting the relevant covariates.