This paper presents a novel framework for modeling reading curiosity, a reader's desire to seek information, from a Natural Language Processing (NLP) perspective. Drawing on Loewenstein's information gap theory, we measure reading curiosity by quantifying semantic information gaps within the semantic structure of a text. Leveraging BERTopic-based topic modeling and persistent homology, we analyze the topological structure (connected elements, cycles, and gaps) of dynamic semantic networks derived from text segments and utilize these features as proxy indicators of information gaps. Experimentally, we collected reading curiosity ratings for S. Collins's novel "The Hunger Games" from 49 participants and used the developed pipeline's topological features as independent variables to build a model to predict these ratings. The results demonstrate a significant improvement in reading curiosity prediction performance (73% explained variance) compared to the baseline model (30% explained variance), validating the validity of the proposed method. This study provides a novel computational method for analyzing the relationship between text structure and reader engagement.