Stochastic network epidemic model and particle filter: General framework and application to influenza in Japan
Parameter inference and state estimation in stochastic and partially observed biological systems remain major problems in mathematical biology. In this work, we introduce a two-dimensional lattice graph model for the spread of infectious diseases. Estimating states and parameters in graph-based stochastic epidemic systems is particularly challenging because of randomness and incomplete observations. To address these issues, we propose a particle filter based data assimilation framework for the sequential estimation of both model states and unknown parameters. Two methodologies are developed: one based on the number of infected agents and another based on partial spatial location's information of infected agents on a two-dimensional lattice. The performance of the two methods are firstly analyzed and validated using synthetic data, and the first method is then applied to influenza data collected from different prefectures in Japan between July 2024 and December 2025. One-week-ahead forecasting simulations are also performed using current weekly data. The findings highlight the effectiveness of the proposed PF framework for real-time epidemic monitoring, forecasting, and adaptive public health decision-making.