Asymptotic behavior for a general class of spreading models
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917059438313472 |
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| author | Chan, K. M. D. Crommelin, D. T. Mandjes, M. R. H. |
| author_facet | Chan, K. M. D. Crommelin, D. T. Mandjes, M. R. H. |
| contents | Growing literatures on epidemic and rumor dynamics show that infection and information coevolve. We present a unified framework for modeling the spread of infection and information: a general class of interaction-driven fluid-limit models expressed as coupled ODEs. The class includes the SIR epidemic model, the Daley-Kendall rumor model, and many extensions. For this general class, we derive theoretical results: under explicit graph-theoretic conditions, we obtain a classification of asymptotic behavior and motivate a conjecture of exponential decay for vanishing states. When these conditions are violated, the classification can fail, and decay may become non-exponential (e.g., algebraic). In deriving the main result, we establish asymptotic stability and $L^1$-integrability properties for state variables. Alongside these results, we introduce the dependency graph that captures outflow dependencies and offers a new angle on the structure of this model class. Finally, we illustrate the results with several examples, including a heterogeneous rumor model and a rumor-dependent SIR model, showing how small changes to the dependency graph can flip asymptotic behavior and reshape epidemic trajectories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior for a general class of spreading models Chan, K. M. D. Crommelin, D. T. Mandjes, M. R. H. Populations and Evolution Dynamical Systems Growing literatures on epidemic and rumor dynamics show that infection and information coevolve. We present a unified framework for modeling the spread of infection and information: a general class of interaction-driven fluid-limit models expressed as coupled ODEs. The class includes the SIR epidemic model, the Daley-Kendall rumor model, and many extensions. For this general class, we derive theoretical results: under explicit graph-theoretic conditions, we obtain a classification of asymptotic behavior and motivate a conjecture of exponential decay for vanishing states. When these conditions are violated, the classification can fail, and decay may become non-exponential (e.g., algebraic). In deriving the main result, we establish asymptotic stability and $L^1$-integrability properties for state variables. Alongside these results, we introduce the dependency graph that captures outflow dependencies and offers a new angle on the structure of this model class. Finally, we illustrate the results with several examples, including a heterogeneous rumor model and a rumor-dependent SIR model, showing how small changes to the dependency graph can flip asymptotic behavior and reshape epidemic trajectories. |
| title | Asymptotic behavior for a general class of spreading models |
| topic | Populations and Evolution Dynamical Systems |
| url | https://arxiv.org/abs/2511.02437 |