Panel count data refers to the research objects that are only observed at discrete time intervals, and frequently appear in recurrent events. When discrete events occur repeatedly, it is of great significance to investigate the influence of covariates on recurrent events. Parameter estimation with the smallest deviation is essential to explain the authenticity of semiparametric regression model, as well as the harm of recurrent events could be decreased by receiving effective regression prediction. The affect of covariates on recurrent events is surveyed using a semiparametric regression model in this study. It has been assumed that the recurrent events, observation process and follow-up process are related to each other, and two latent variables are applied to represent the relationship among the three processes, with supposing the two latent variables following Dirichlet process, in order to establish a joint model. To solve the parameter estimation in common, the EM and MCMC algorithms are utilized, and the accuracy of parameter estimation with respect to our model is compared to that of other models. Lastly, the data of COVID-NET has been used for exploring the effect of four factors, including age, gender, race, and whether patients have potential diseases, as covariates on repeated hospitalization.