Perron-Volterra Lyapunov functions and competitive exclusion partitions in n-strain models with diagonal Metzler transversal Jacobian and rank-one blocks

Abstract

For multi-strain models with increasing concave incidence and scalar, uncorrelated strain blocks, we prove a competitive-exclusion partition of parameter space, by constructing explicit global Lyapunov functions for the boundary and coexistence equilibria. We further extend the construction to models containing one irreducible rank-one infection block and several uncorrelated scalar strains. Our method combines Volterra entropy terms for the resident variables with Perron-weighted linear functionals for the invading variables, whose weights are obtained from transversal Metzler Jacobians on boundary faces. We have provided an algorithmic implementation in the Mathematica package E PID CRN (https:// github.com/florinav/EpidCRNmodels). The method organizes the dynamics via the minimal siphon lattice, recursively computes Perron eigenvectors of transversal Jacobians, and constructs candidate Lyapunov functions for all equilibria, producing a parameter partition into regions with a unique locally stable equilibrium and, for n = 2, explicit global stability certificates.