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Zbl 1025.92011
d'Onofrio, A.
Pulse vaccination strategy in the SIR epidemic model: Global asymptotic stable eradication in presence of vaccine failures. (English)
[J] Math. Comput. Modelling 36, No.4-5, 473-489 (2002). ISSN 0895-7177

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 {\it 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 2000:: *92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K45 Equations with impulses
34D23 Global stability

Keywords: deterministic epidemic models; stability theory; impulsive differential equations; vaccinations

Citations: Zbl 1043.92527

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