Explicit minimum wave-speed formulas for cooperative go-or-grow systems

Derive explicit closed-form expressions for the minimum traveling-wave speed in cooperative instances of the general go-or-grow reaction–diffusion system for migrating cells u and proliferating cells v, beyond the variational characterization \bar c = inf_{ρ>0} λ_A(ρ)/ρ, and identify parameter regimes under which such explicit formulas hold.

Background

For cooperative go-or-grow systems, the paper provides a linear-spread-rate formula expressed as the infimum over a spectral quantity, which in special cases coincides with known expressions.

The authors ask when one can move beyond this variational characterization to obtain explicit closed-form speed formulas, a problem that remains unresolved in general.