Survey on mathematical modeling of infectious disease dynamics: insights and applications

Mathematical modeling has become an indispensable tool for understanding, predicting, and controlling the spread of infectious diseases. Over the years, a wide variety of models have been developed to analyze disease dynamics and forecast epidemic trajectories. Deterministic and stochastic frameworks provide quantitative insights into transmission mechanisms and allow for rigorous evaluation of public health interventions such as quarantine, vaccination, and lockdown strategies. The integration of computational and data-driven methods has significantly advanced epidemic modeling. Techniques from network analysis, large-scale data processing, and artificial intelligence (AI) have improved both the accuracy and efficiency of model predictions. In particular, deep learning methods-most notably in medical imaging-enable fast and reliable automated diagnosis of disease. Moreover, the combination of mathematical modeling with AI facilitates real-time tracking and forecasting of outbreaks, thereby supporting public health authorities in optimizing resource allocation and ensuring timely responses. The increasing availability of open-source datasets, including case reports, demographic information, mobility patterns, and medical images, has further expanded the capabilities of data-driven epidemic models. Such approaches play a critical role in managing emerging infectious diseases, strengthening preparedness, and mitigating the societal impact of future outbreaks. This work provides a comprehensive overview of mathematical modeling approaches in infectious disease dynamics, emphasizing their relevance for public health emergency management and evidence-based intervention strategies.