On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination.

*(English)* Zbl 1219.34066
Summary: This paper discusses the disease-free and endemic equilibrium points of a SVEIRS propagation disease model which potentially involves a regular constant vaccination. The positivity of such a model is also discussed as well as the boundedness of the total and partial populations. The model takes also the natural population growth and the mortality associated to the disease as well as the loss of immunity of newborns into consideration. It is assumed that there are two finite delays affecting the susceptible, recovered, exposed, and infected population dynamics. Some extensions are given for the case when impulsive nonconstant vaccination is incorporated at, in general, an aperiodic sequence of time instants. Such an impulsive vaccination consists of a culling or a partial removal action on the susceptible population which is transferred to the vaccinated one. The oscillatory behavior under impulsive vaccination, performed in general, at nonperiodic time intervals, is also discussed.

##### MSC:

34C60 | Qualitative investigation and simulation of models (ODE) |

92D30 | Epidemiology |

92C60 | Medical epidemiology |

34C05 | Location of integral curves, singular points, limit cycles (ODE) |

34A37 | Differential equations with impulses |

34C25 | Periodic solutions of ODE |

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