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Zbl 1034.92025
Arino, Julien; McCluskey, C. Connell; van den Driessche, P.
Global results for an epidemic model with vaccination that exhibits backward bifurcation. (English)
[J] SIAM J. Appl. Math. 64, No. 1, 260-276 (2003). ISSN 0036-1399; ISSN 1095-712X/e

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.

MSC 2000:: *92C60 Medical epidemiology
92D30 Epidemiology
34D23 Global stability
34C23 Bifurcation (periodic solutions)
34C60 Applications of qualitative theory of ODE
37N25 Dynamical systems in biology

Keywords: vaccination; backward bifurcation; compound matrices; global dynamics

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