Arino, Julien; McCluskey, C. Connell; van den Driessche, P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. (English) Zbl 1034.92025 SIAM J. Appl. Math. 64, No. 1, 260-276 (2003). Summary: Vaccination of both newborns and susceptibles is included in a transmission model for a disease that confers immunity. The interplay of the vaccination strategy together with the vaccine efficacy and waning is studied. In particular, it is shown that a backward bifurcation leading to bistability can occur. Under mild parameter constraints, compound matrices are used to show that each orbit limits to an equilibrium. In the case of bistability, this global result requires a novel approach since there is no compact absorbing set. Cited in 1 ReviewCited in 167 Documents MSC: 92C60 Medical epidemiology 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 37N25 Dynamical systems in biology Keywords:vaccination; backward bifurcation; compound matrices; global dynamics PDFBibTeX XMLCite \textit{J. Arino} et al., SIAM J. Appl. Math. 64, No. 1, 260--276 (2003; Zbl 1034.92025) Full Text: DOI