On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls.

*(English)*Zbl 1219.34104Summary: This paper discusses a generalized time-varying SEIR disease propagation model subject to delays which potentially involves mixed regular and impulsive vaccination rules. The model takes also into account the natural population growth and the mortality associated to the disease, and the potential presence of disease endemic thresholds for both the infected and infectious population dynamics as well as the loss of immunity of newborns. The presence of outsider infections is also considered. It is assumed that there is a finite number of time-varying distributed delays in the susceptible-infected coupling dynamics influencing the susceptible and infected differential equations. It is also assumed that there are time-varying point delays for the susceptible-infected coupled dynamics influencing the infected, infectious, and removed-by-immunity differential equations. The proposed regular vaccination control objective is the tracking of a prescribed suited infectious trajectory for a set of given initial conditions. The impulsive vaccination can be used to improve discrepancies between the SEIR model and a suitable reference one.

##### MSC:

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

92D30 | Epidemiology |

92C60 | Medical epidemiology |

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

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