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Daniel Precioso, PhD
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Remove redundant Daley-Kendall model reference from SIS section and add it to SIR section for clarity and improved organization.
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modules/networks/index.qmd

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Susceptible → Infected → Recovered
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Permanent immunity.
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If you want one extra reference beyond SIR, a classical rumor counterpart is the **Daley-Kendall** model (Ignorant → Spreader → Stifler), where spreaders become stiflers after contact with spreaders/stiflers [@daley1965stochastic].
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Key questions you will answer:
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* How does network structure affect epidemic size?

modules/networks/sir.qmd

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In SIS, $I \to S$ (you become susceptible again). In SIR, $I \to R$ (you become immune). That single change completely changes the *long-term* behavior.
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:::
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## A key rigorous fact (absorbing states)
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### Related Rumor Model
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If you want one extra reference beyond SIR, a classical rumor counterpart is the **Daley-Kendall** model (Ignorant -> Spreader -> Stifler), where spreaders become stiflers after contact with spreaders/stiflers [@daley1965stochastic].
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## Absorbing States
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On a finite graph with $\mu > 0$, the process reaches a time $T$ such that there are **no infected nodes** ($I(T)=0$), and after that nothing can ever change [@keeling2008modeling; @pastor2015epidemic].
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Intuition (but still rigorous): each node can become infected **at most once** (because $R$ is permanent), so there can be at most $N$ infection events. Since recovery happens with positive probability, infections cannot persist forever.
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Each node can become infected **at most once** (because $R$ is permanent), so there can be at most $N$ infection events. Since recovery happens with positive probability, infections cannot persist forever.
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This means SIR always ends in a "frozen" configuration containing only $S$ and $R$ nodes.
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