Global stability of SEIRS models in epidemiology. (English) Zbl 0976.92020

Summary: SEIRS epidemiological models with general nonlinear incidence in a constant population are studied. Under the restriction that the rate of loss of immunity is either sufficiently small or sufficiently large, global asymptotic stability of the endemic equilibrium when it is unique is proved using a geometric approach to global stability for nonlinear autonomous systems. For the special case of bilinear incidence, this global result completes determination of a sharp threshold for the classical SEIRS model under the above restriction.


92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations