On the existence of a nontrivial equilibrium in relation to the basic reproductive number - Wijaya, Karunia Putra; Sutimin; Soewono, Edy; Götz, Thomas (Zielona Góra: Uniwersytet Zielonogórski)
Equilibrium analysis in autonomous evolutionary models is of central importance for developing long term treatments. This task typically includes checks on the existence and stability of some equilibria. Prior to touching on the stability, one often attempts to determine the existence where the basic reproductive number R0 plays a critical role as a threshold parameter. When analyzing a nontrivial equilibrium (e.g., an endemic, boundary, or coexistence equilibrium) where R0 is explicit, we usually come across a typical result: if R0 > 1, then a nontrivial equilibrium exists in the biological sense.
Keywords: autonomous model; nontrivial equilibrium; basic reproductive number; nonlinear eigenvalue problem