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

Overview

Mathematical modeling of infectious disease dynamics constitutes a systematic framework for quantifying transmission mechanisms, forecasting epidemic trajectories, and evaluating public health interventions. Deterministic and stochastic modeling approaches provide complementary perspectives on disease spread at population and individual levels. The field has evolved substantially through integration of computational methods, network analysis, and data-driven techniques, enabling more precise characterization of complex epidemic phenomena.

Methods and approach

The survey encompasses deterministic and stochastic mathematical frameworks applied to infectious disease transmission. Computational and data-driven methodologies, including network analysis, machine learning, and deep learning techniques, are integrated to enhance model accuracy and predictive capacity. Network-based approaches characterize contact structures and transmission pathways. Deep learning methods facilitate automated diagnosis through medical imaging analysis. Integration of open-source epidemiological datasets—including case reports, demographic information, mobility patterns, and medical imaging data—enables parameterization of mechanistic and empirical models. Real-time data assimilation and computational optimization support model calibration and validation.

Key Findings

Mathematical modeling frameworks demonstrate efficacy in quantifying disease transmission parameters, predicting epidemic trajectories under various scenarios, and evaluating intervention effectiveness. Incorporation of computational and artificial intelligence methods substantially improves prediction accuracy and computational efficiency. Network analysis reveals heterogeneous transmission patterns dependent on contact structure and population mobility. Deep learning approaches achieve rapid and accurate automated diagnosis, supporting early case identification. Integration of data-driven methods with mechanistic modeling enables real-time epidemic forecasting and scenario analysis for resource allocation optimization.

Implications

Mathematical modeling approaches provide quantitative evidence for public health decision-making regarding intervention strategies including quarantine, vaccination, and mobility restrictions. Enhanced predictive capacity through computational and machine learning integration supports timely and targeted resource allocation by public health authorities. Real-time forecasting and outbreak tracking capabilities strengthen epidemic preparedness and response coordination. Integration of heterogeneous data sources and AI techniques facilitates adaptive management of emerging infectious diseases.