The gene expression profiles of distinct cell types reflect complex genomic interactions among multiple simultaneous biological processes within each cell that can be altered by disease progression as well as genetic background. The identification of these active cellular programs is an open challenge in the analysis of single-cell RNA-seq data. Latent Dirichlet Allocation (LDA) is a generative method used to identify recurring patterns in counts data, commonly referred to as topics that can be used to interpret the state of each cell. However, LDA's interpretability is hindered by several key factors including the hyperparameter selection of the number of topics as well as the variability in topic definitions due to random initialization. We developed Topyfic, a Reproducible LDA (rLDA) package, to accurately infer the identity and activity of cellular programs in single-cell data, providing insights into the relative contributions of each program in individual cells. We apply Topyfic to brain single-cell and single-nucleus datasets of two 5xFAD mouse models of Alzheimer's disease crossed with C57BL6/J or CAST/EiJ mice to identify distinct cell types and states in different cell types such as microglia. We find that 8-month 5xFAD/Cast F1 males show higher level of microglial activation than matching 5xFAD/BL6 F1 males, whereas female mice show similar levels of microglial activation. We show that regulatory genes such as TFs, microRNA host genes, and chromatin regulatory genes alone capture cell types and cell states. Our study highlights how topic modeling with a limited vocabulary of regulatory genes can identify gene expression programs in single-cell data in order to quantify similar and divergent cell states in distinct genotypes.