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Symbolic computation of action functionals for multi-dimensional CRN/ME Hamiltonian systems

Determine whether closed-form (symbolic) computation of the action functional governing expected escape times is possible for multi-dimensional cases beyond the SI process in the Hamiltonian framework associated with chemical reaction networks and epidemic models.

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Background

The paper outlines a Hamiltonian approach to estimate escape paths and expected travel times in stochastic CRN/ME systems, where the action functional characterizes asymptotic scaling of escape times.

While an explicit solution is known for the SI process, the authors note that in higher-dimensional settings only numerical integration seems to work; it remains unknown whether symbolic solutions exist in other specific cases.

References

Whether or not symbolic treatment is possible in other particular cases is an open problem.

— Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them (2411.00488 - Avram et al., 1 Nov 2024) in Section “The CRN representation yields a Hamiltonian representation of the expected time spent along escape paths of stochastic CTMC processes”