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Pulse vaccination strategy in the SIR epidemic model: Global asymptotic stable eradication in presence of vaccine failures. (English) Zbl 1025.92011
Summary: We study the use of a pulse vaccination strategy to eradicate infectious diseases modelizable by SIR epidemic models. We demonstrate the global asymptotic stability of the eradication solution [which was conjectured by L. Stone et al., Math. Comput. Modelling 31, 207-215 (2000; Zbl 1043.92527), for pulse vaccination in the classical SIR model] for a general model in which non-permanent immunization, variations of the total population size, and the emerging problem of vaccine failures are considered. As a strategy using a second inoculation as a standard practice, we propose a model to describe a modification of this strategy including the second inoculation and we study its local asymptotic stability.
MSC:
92D30Epidemiology
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
34D23Global stability of ODE