R_0, the dominant eigenvalue of the recovery-rate-normalized interaction matrix, triggers a transcritical bifurcation: disease-free equilibrium is globally stable for R_0 ≤ 1 and unstable with a unique stable endemic equilibrium for R_0 > 1.
Analysis, prediction, and control of epidemics: A survey from scalar to dynamic network models
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On the dynamic behavior of the network SIRS epidemic model
R_0, the dominant eigenvalue of the recovery-rate-normalized interaction matrix, triggers a transcritical bifurcation: disease-free equilibrium is globally stable for R_0 ≤ 1 and unstable with a unique stable endemic equilibrium for R_0 > 1.