Manufacturing of recombinant adeno-associated virus (rAAV) viral vectors remains challenging, with low yields and low full:empty capsid ratios in the harvest. To elucidate the dynamics of recombinant viral production, we develop a mechanistic model for the synthesis of rAAV viral vectors by triple plasmid transfection based on the underlying biological processes derived from wild-type AAV. The model covers major steps starting from exogenous DNA delivery to the reaction cascade that forms viral proteins and DNA, which subsequently result in filled capsids, and the complex functions of the Rep protein as a regulator of the packaging plasmid gene expression and a catalyst for viral DNA packaging. We estimate kinetic parameters using dynamic data from literature and in-house triple transient transfection experiments. Model predictions of productivity changes as a result of the varied input plasmid ratio are benchmarked against transfection data from the literature. Sensitivity analysis suggests that (1) the poorly coordinated timeline of capsid synthesis and viral DNA replication results in a low ratio of full virions in harvest, and (2) repressive function of the Rep protein could be impeding capsid production at a later phase. The analyses from the mathematical model provide testable hypotheses for evaluation and reveal potential process bottlenecks that can be investigated.