Minimal infection set for R0 computation

Determine conditions under which a proper subset of infection/invading species suffices to compute the basic reproduction number R0 without changing its value, and characterize such "R0-sufficient minimal infection sets" potentially via Petri net siphons.

Background

Empirical observations indicate that R0 can sometimes be computed from a reduced set of infection variables, simplifying analysis. However, formal criteria identifying when such reduction is valid are lacking.

The authors suggest a possible connection to siphons in Petri nets, motivating structural characterizations of minimal infection sets that preserve R0.

References

Open Problem 4. It has been observed in [AABJ23] and before that sometimes selecting only a subset of the infection/invading species leaves Ro unchanged, while reducing the computations. Understanding when an "Ro sufficient minimal infection set", different form the total infection set, exists, is an open problem, which might be related to the concept of siphons of the associated Petri net [ADLS07].

— Stability in Reaction Network Models via an Extension of the Next Generation Matrix Method (2411.11867 - Avram et al., 3 Nov 2024) in Section 4.4