tetano
Editor, Senior Moderator
Math Biosci
. 2026 Nov 10:109853.
doi: 10.1016/j.mbs.2026.109853. Online ahead of print.
Ihtisham Ul Haq 1 , Serge Richard 2
Affiliations Expand
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 Perturbation-based Particle Filter (PPF) 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 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. The second method is tested only with synthetic data since the real data considered do not include the required location information. We also compare the two proposed methods with the Sampling Importance Resampling Particle Filter (SIR-PF). The results show that both methods provide more accurate estimates compared to the SIR-PF. One-week-ahead forecasting simulations are also performed using current weekly data. The findings highlight the effectiveness of the proposed PPF framework for real-time epidemic monitoring, forecasting, and adaptive public health decision-making.
Keywords: 2D lattice graph model; influenza; particle filter; stochastic epidemic model.
. 2026 Nov 10:109853.
doi: 10.1016/j.mbs.2026.109853. Online ahead of print.
Stochastic network epidemic model and perturbation-based particle filter: Application to influenza in Japan
Ihtisham Ul Haq 1 , Serge Richard 2
Affiliations Expand
- PMID: 43008931
- DOI: 10.1016/j.mbs.2026.109853
Abstract
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 Perturbation-based Particle Filter (PPF) 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 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. The second method is tested only with synthetic data since the real data considered do not include the required location information. We also compare the two proposed methods with the Sampling Importance Resampling Particle Filter (SIR-PF). The results show that both methods provide more accurate estimates compared to the SIR-PF. One-week-ahead forecasting simulations are also performed using current weekly data. The findings highlight the effectiveness of the proposed PPF framework for real-time epidemic monitoring, forecasting, and adaptive public health decision-making.
Keywords: 2D lattice graph model; influenza; particle filter; stochastic epidemic model.