Recent Advances in Mathematical Epidemiology and Applications

Dear Colleagues,

In today's highly interconnected world, human social activities have become increasingly frequent and cross-border mobility has grown more efficient and convenient. Whether through rail transport or international air travel networks, the unprecedented flow of people and goods has significantly intensified the connections between global regions. This deep interconnectivity not only facilitates rapid economic and informational exchange but also creates new "pathway networks" for the cross-border transmission of infectious diseases, giving rise to a new paradigm of disease spread.

Over the past 50 years, the frequent emergence of major epidemics—such as SARS, H1N1, and COVID-19—has highlighted the heightened risk of localized outbreaks evolving into global pandemics in an era of high social mobility. This poses a long-term challenge to infectious disease prevention and control. In the early stages of an outbreak, pharmaceutical interventions such as medication and vaccines often cannot respond swiftly. The development of treatments for novel diseases or emerging variants is time-consuming, and the efficacy of vaccines may be uncertain. As a result, non-pharmaceutical interventions (NPIs) become the primary strategy for curbing the spread of infection during the initial phases.

The effective implementation of NPIs relies heavily on accurate modeling and predictive analysis of disease transmission processes. From classical models like SIR and SEIR to population-stratified models and regional transmission simulations tailored to specific diseases, the theoretical and methodological frameworks for infectious disease modeling have continued to evolve. These models enhance our understanding of transmission chains, support the assessment of intervention strategies, and provide quantitative evidence to inform policy decisions.

As we enter the data-driven era, artificial intelligence (AI) and machine learning technologies are increasingly integrated with traditional mathematical models, giving rise to a new modeling paradigm that combines mechanism-driven and data-driven approaches. In recent years, the following has been achieved:

• Sequence modeling techniques such as long short-term memory (LSTM) and gated recurrent units (GRU) have been widely applied to epidemic time series forecasting.
• The transformer architecture has enhanced the ability to learn long-term dependencies and cross-regional transmission patterns.
• Graph neural networks (GNNs) enabled structured modeling of complex contact networks and transmission pathways.
• Multi-source data fusion techniques—incorporating mobility data, social media signals, and clinical records—have significantly improved the timeliness and robustness of modeling efforts.

From the perspective of “past–present–future,” infectious disease modeling is undergoing a transition from classical mathematical theories to the challenges of high-dimensional and complex systems. This Special Issue serves as a significant academic convergence, aiming to systematically review and synthesize the innovative applications of both traditional dynamical models and modern AI tools in the context of infectious disease modeling. It seeks to build a solid theoretical foundation and a robust modeling toolkit in preparation for potential future pandemic threats.

Prof. Dr. Chitin Hon
Guest Editor

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• mathematical epidemiology
• infectious disease modeling
• SEIR/SIR models
• machine learning in epidemiology
• LSTM/transformer models
• epidemic forecasting
• AI-augmented mathematical models
• global mobility and disease spread
• signal analysis
• kinetic equation
• deep learning