A systematic review of mathematical and machine learning models of Avian Influenza.

Avian influenza (AI) is a highly transmissible disease with significant implications for public health, agriculture, and global food security. Mathematical, statistical, and machine learning-based models play a crucial role in understanding AI dynamics, predicting outbreaks, and evaluating intervention strategies. This systematic review assesses existing modeling approaches, categorizing studies into mathematical and statistical models, machine learning-based models, and hybrid models, with a focus on their applications in risk assessment, outbreak prediction, dynamic modeling, and parameter estimation. Following the PRISMA guidelines, a comprehensive literature search was conducted in PubMed/MEDLINE, Scopus, Web of Science, and Embase. The search strategy included machine learning-related terms combined with modeling approaches such as compartmental models (e.g., SEIR, SIR), statistical methods, machine learning algorithms (e.g., SVM, Random Forest, XGBoost), and hybrid frameworks. A total of 43 studies met the inclusion criteria: 26 (60.47 %) used mathematical/statistical models, 12 (27.91 %) used machine learning models, and 5 (11.63 %) employed hybrid models. Among mathematical/statistical models, 50 % addressed transmission dynamics, while machine learning models primarily focused on risk assessment (50 %) and outbreak prediction (41.67 %). Hybrid models, though less prevalent, contributed to enhanced prediction accuracy and understanding of transmission. However, validation remains inconsistent, with 25.58 % of mathematical/statistical models lacking explicit validation. Sensitivity analysis and numerical simulations dominate mathematical and statistical model validation, whereas machine learning studies commonly use F1-score, confusion matrices, and external validation datasets. Persistent challenges include limited generalizability of datasets, inconsistency in validation protocols, and high computational costs. This review highlights the need for enhanced data sharing, integration of environmental and real-time information, standardized validation methods, and further development of hybrid approaches to strengthen model reliability and improve the prediction and control of future AI outbreaks.