Presentation Information
[SS12-03]Epidemic Models on Networks and the Basic Reproduction Number
*Satoru Morita1 (1. Shizuoka University (Japan))
Keywords:
network science,basic reproduction number,epidemic models on networks
The structure of human interactions plays a fundamental role in the spread of infectious diseases. While classical epidemic models often assume homogeneous mixing, real-world contact patterns are highly heterogeneous and are best represented as complex networks. Incorporating network structures into epidemic models has led to significant advancements in epidemic threshold analysis, outbreak prediction, and intervention strategies. Understanding how contact heterogeneity, degree correlations, and clustering influence disease dynamics is therefore crucial for refining epidemic forecasts and control measures.
In this presentation, I will first introduce a generalized compartmental model (including SIS, SIR, SEIR models, etc.) on networks, where the infection process is explicitly structured by the underlying contact network [1]. By formulating the disease dynamics as a Markov process, I will derive a comprehensive expression for the basic reproduction number that extends beyond classical epidemic models. This approach allows for a unified treatment of a wide range of epidemiological scenarios, including models with latent periods, waning immunity, or multiple infection stages.
The second part of the talk will introduce a spectral approach to studying network structure, with a focus on degree correlations and their impact on epidemic dynamics [2]. Using eigenvalue decomposition, I will present a formalism that accounts for degree-degree correlations and refines epidemic threshold calculations. This method provides a more precise characterization of disease spread on structured networks compared to traditional mean-field approximations.
I look forward to discussing with participants how these mathematical approaches can contribute to a deeper understanding of epidemic dynamics on networks. In particular, I hope to explore potential applications and limitations of the proposed framework, as well as future directions for integrating network-based epidemiological models with real-world data.
[1] Satoru Morita, Basic reproduction number of epidemic models on sparse networks. Phys. Rev. E 106, 034318 (2022).
[2] Satoru Morita, Representation of degree correlation using eigenvalue decomposition and its application to epidemic models. Prog. Theor. Exp. Phys. 2023, 111J01 (2023).
In this presentation, I will first introduce a generalized compartmental model (including SIS, SIR, SEIR models, etc.) on networks, where the infection process is explicitly structured by the underlying contact network [1]. By formulating the disease dynamics as a Markov process, I will derive a comprehensive expression for the basic reproduction number that extends beyond classical epidemic models. This approach allows for a unified treatment of a wide range of epidemiological scenarios, including models with latent periods, waning immunity, or multiple infection stages.
The second part of the talk will introduce a spectral approach to studying network structure, with a focus on degree correlations and their impact on epidemic dynamics [2]. Using eigenvalue decomposition, I will present a formalism that accounts for degree-degree correlations and refines epidemic threshold calculations. This method provides a more precise characterization of disease spread on structured networks compared to traditional mean-field approximations.
I look forward to discussing with participants how these mathematical approaches can contribute to a deeper understanding of epidemic dynamics on networks. In particular, I hope to explore potential applications and limitations of the proposed framework, as well as future directions for integrating network-based epidemiological models with real-world data.
[1] Satoru Morita, Basic reproduction number of epidemic models on sparse networks. Phys. Rev. E 106, 034318 (2022).
[2] Satoru Morita, Representation of degree correlation using eigenvalue decomposition and its application to epidemic models. Prog. Theor. Exp. Phys. 2023, 111J01 (2023).