This volume presents a comprehensive compilation of chapters whose topics were presented at the 2nd International Conference on Mathematical Analysis and Application in Modeling (CMAAM-2023), held at the Department of Mathematics & the Center for Mathematical Biology and Ecology, Jadavpur University, Kolkata, West Bengal, India, from 9–11 October 2023. It encompasses groundbreaking research on cutting-edge developments across various branches of mathematics and its applications in diverse disciplines. In the realm of epidemiology, the book delves into the utilization of advanced tools such as fractional calculus, optimal control therapy and impulse therapeutic approaches. These tools, integrated with mathematical models, offer innovative solutions for managing various diseases and optimizing drug dose regimens. Beyond the scope of epidemiology, the book also incorporates chapters elucidating fundamental concepts in pure mathematics. These include explorations of topological phenomena and diverse algebraic concepts. This dual focus on applied mathematics and pure mathematical principles enhances the book's usability, catering to a broad audience of researchers and scholars. The book primarily targets young researchers engaged in the specified areas of study. By bridging the gap between theoretical mathematics and real-world applications, it serves a valuable resource, providing insights and methodologies that contribute to advancements in research and application across multiple disciplines.