| Summary: | This paper deals with a stochastic Susceptible-Infective-Vaccinated-Susceptible (<i>SIVS</i>) model with infection reintroduction. Health policies depend on vaccine coverage, <inline-formula> <math display="inline"> <semantics> <msub> <mi>v</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula>, that guarantees herd immunity levels in the population. Vaccine failures occur when an organism develops a disease despite of being vaccinated against it. After vaccination, a proportion of healthy individuals unsuccessfully tries to increase antibody levels and, consequently these individuals are not immune to the vaccine preventable disease. When an infectious process is in progress, the initial vaccine coverage drops down and herd immunity will be lost. Our objective was to introduce a warning vaccination level and define random measures quantifying the time until the number of vaccinated descends to a warning vaccination level (i.e., the so-called sleeping period), and the epidemic size. A sensitivity analysis was performed to assess the influence of the model parameters on the variation and robustness of the sleeping period and the number of infections observed within it.
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