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Carl T. Bergstrom May 2
1. Yesterday, and I published an OpEd in the explaining the concept of overshoot: an epidemic doesn't magically stop when you reach herd immunity.
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Carl T. Bergstrom
2. Because the aim was to explain a simple concept, we included a figure based on the simplest model that captures the phenomenon of interest: a basic SIR model. We set R0=3 and plotted the trajectory. (An SEIR model has the same herd immunity threshold and final % infected.)
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Carl T. Bergstrom May 2
Replying to @CT_Bergstrom
3. Some people have raised concerns about whether a basic SIR model adequately captures the qualitative features and basic quantitative magnitudes of a real-world system with heterogeneous individual parameters and a realistic contact network instead of a well-mixed structure.
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Carl T. Bergstrom May 2
Replying to @RS_McGee
4. If it failed to do so, the SIR approximation might be misleading. We've spent the past two months developing a stochastic SEIR modeling framework with for age structure, network structure, and population heterogeneity. Lead developer šŸ§µ:
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Carl T. Bergstrom May 2
Replying to @CT_Bergstrom
5. In short, the model includes age structure, age-specific interactions (workplaces, schools, etc.), multiple network layers of hierarchically structured contacts, family structure, and heterogeneity in individual social and biological parameters.
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Carl T. Bergstrom May 2
Replying to @CT_Bergstrom
6. Network structure and all biological parameter distributions are all estimated from empirical data, as is household composition. The contact network structure regenerates empirical distributions of age-by-age encounter rates.
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Carl T. Bergstrom May 2
Replying to @CT_Bergstrom
7. A framework like this is be essential for exploring the effects of age-specific interventions (e.g. cocooning) and network-based interventions (e.g. contact tracing). But I've found it remarkable how little the heterogeneity and network structure impact basic epi dynamics.
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Carl T. Bergstrom May 2
Replying to @nytimes
8. Hence my confidence in using a simple SIR model to illustrate concepts such as herd immunity and overshoot in the OpEd. The bottom line is that these details don't change things qualitatively and barely shift the quantitative values.
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Carl T. Bergstrom May 2
Replying to @CT_Bergstrom
9. To illustrate, below is the scenario from the OpEd SIR model (R=3, no interventions), implemented in our stochastic age-stratified network model with empirically-estimated levels of population heterogeneity for all parameters.
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Carl T. Bergstrom May 2
Replying to @CT_Bergstrom
10. Compared to the SIR model, the herd immunity threshold is a few percent lower, as is the final fraction infected. But all qualitative features are preserved, and the quantitative values are very similar. I hope this will put some of the concerns to rest.
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Ray May 3
Replying to @CT_Bergstrom
Have to start with the the easiest to understand Can't jump into differential equations
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Data dude May 8
Too many ODEs are never enough....
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