This volume gathers selected papers presented at the IC-MSQUARE 2024 - 13th International Conference on Mathematical Modeling in Physical Sciences held in Kalamata, Greece from September 30–October 3, 2024. This proceedings volume offers a compilation of cutting-edge research, which aims to advance the knowledge and development of high-quality research in mathematical fields related to physics, chemistry, biology, medicine, economics, environmental sciences, and more. Annually held since 2012, the IC-MSQUARE conference serves as a platform for the exchange of ideas and discussions on the latest technological trends in these fields. This book is an invaluable resource for researchers, academicians, and professionals in these areas seeking to stay up-to-date with the latest developments in mathematical modeling.