Global Stability in Some Seir Epidemic Models

The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon. If the basic reproduction number R₀ is below unity, the disease-free equilibrium P₀ is globally stable in the feasible region and the disease always dies out. If R₀ > 1, a unique endemic equilibrium P_* is globally asymptotically stable in the interior of the feasible region and the disease will persist at the endemic equilibrium if it is initially present. In this paper, this threshold phenomenon is established for two epidemic models of SEIR type using two recent approaches to the global-stability problem.