How is R0 defined in terms of the states? (Scenario 2)

[liunelson]

If relevant, page 2 of this PDF shows how R0 can be derived from the rate parameters in a SIR model: https://web.stanford.edu/~jhj1/teachingdocs/Jones-on-R0.pdf

[liunelson]

Oh wait, you're asking for Scenario 2 Question 2.b.ii.

[liunelson]

Eq. 1 here defines an instantaneous R values from S(t) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7325187/

[YingboMa]

@liunelson How can we get:

D the mean duration of infectiousness

[liunelson]

@YingboMa The SIDARTHE-V paper actually defines it right after Fig. 2: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8205853/

the effective reproduction number Reff(t) = R0 * S(t) goes below 1 due to the decreasing susceptible fraction S(t); hence, the epidemic is eventually suppressed

R0 is defined in the methods section:

parametric reproduction number R0 is the H∞ norm of the positive system from u to ys with parameters tuned at the beginning of the epidemic...

[Free-Quarks]

https://drive.google.com/file/d/1es3vJlB3ExvOmigpVG3-Op1TeCDUwgyP/view?usp=share_link

[Free-Quarks]

that screen shot is from this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7175834/pdf/41591_2020_Article_883.pdf

[liunelson]

@YingboMa Please clarify what R0 and Reff(t) definition you are using. Based on the SIDARTHE-V, R0 = beta/gamma and Reff(t) = R0 * S(t) where R0 = lim(t -> 0) Reff(t). Your earlier notebook used some random D value?

[YingboMa]

R0 is defined as this https://github.com/ChrisRackauckas/ASKEM_Evaluation_Staging/pull/57#issue-1565304425 i.e. pg 8 of https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8205853/pdf/41591_2021_Article_1334.pdf

And R_t = R0 * S

[YingboMa]

I haven't updated the notebook yet because the updated question from MITRE is still ill-formed.