Dice Question Streamline Icon: https://streamlinehq.com

Extend rank-one SIR-PH-FA relations to higher-rank NGMs or multiple susceptible types

Ascertain whether formulas analogous to the rank-one SIR-PH-FA relations—such as R0 equaling the product of the disease-free susceptible level and the replacement number, and the endemic susceptible fraction equaling the reciprocal of the replacement number—hold for models whose next generation matrix has higher rank or that include multiple types of susceptibles.

Information Square Streamline Icon: https://streamlinehq.com

Background

For SIR-PH-FA models with a single susceptible class and a rank-one next generation matrix, the authors establish simple relations linking R0, the disease-free susceptible level, the endemic susceptible level, and the replacement number.

It is unknown whether similar closed-form relationships persist in more general settings with higher-rank NGMs or multiple susceptible classes.

References

Open Problem

Are there formulas analogous to \eqr{R0sR}, \eqr{sEACR}, \eqr{R0fr}, in the case of higher rank NGMs, or several type of susceptibles?

— Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them (2411.00488 - Avram et al., 1 Nov 2024) in Open Problem, Subsection “Markovian Semi-Groups Associated to SIR-PH-FA Models …”