Stability properties of pulse vaccination strategy in SEIR epidemic model.

*(English)*Zbl 0991.92025Summary: The problem of the applicability of the pulse vaccination strategy (PVS) for the stable eradication of some relevant general class of infectious diseases is analyzed in terms of the study of local asymptotic stability (LAS) and global asymptotic stability (GAS) of the periodic eradication solution for the SEIR epidemic model in which is included the PVS. Demographic variations due or not to disease-related fatalities are also considered. Due to the non-triviality of the Floquet’s matrix associate to the studied model, the LAS is studied numerically and in this way it is found a simple approximate (but analytical) sufficient criterion which is an extension of the LAS constraint for the stability of the trivial equilibrium in SEIR models without vaccination. The numerical simulations also seem to suggest that the PVS is slightly more efficient than the continuous vaccination strategy. Analytically, the GAS of the eradication solutions is studied and it is demonstrated that the above criteria for the LAS guarantee also the GAS.

##### MSC:

92D30 | Epidemiology |

34D05 | Asymptotic properties of solutions to ordinary differential equations |

92C60 | Medical epidemiology |

34D23 | Global stability of solutions to ordinary differential equations |

##### Keywords:

vaccination models; impulsive differential equations; Hill’s differential equation; cooperative systems
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##### References:

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