Repeated measures are often collected in longitudinal follow-up from clinical trials and observational studies. Motivated by the Assessment, Serial Evaluation, and Subsequent Sequelae of Acute Kidney Injury (ASSESS-AKI) study, recurrent events of AKI could occur more frequently for the subject with deteriorated kidney function in particular after the first episode of AKI; however, some subjects may not experience any AKI events. Therefore, the number of associated kidney function measures (i.e., serum creatinine) during hospitalized AKI recurrence varies across subjects, which could be correlated with the overall kidney outcome, resulting in an informative cluster size. Meanwhile, a high percentage of zero AKI recurrences are detected from this study, thus, we propose a joint modeling approach of longitudinal data and zero-inflated informative cluster size by considering a terminal event as a covariate. The parameter estimation is obtained by using a three-stage semi-parametric likelihood-based approach. Extensive simulations are conducted, and a real data application on the ASSESS-AKI is provided in the end.